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8. Important formula:  sin (A+B)=sin A. cos B+ cos A.sin B  (0)  (a)  (b) sin (A-B) sinA.cos B-cosA.sin B  (g)  (0)  (c)  cos(A+B) cosA.cosB-sinA.sin (d) cos(A-B)=cosA.cosB+sinAsinB  9.  tan(A+B)= tan A+tan B  (e)  1-tan A. tan B  (a)  tan(A-B)-tan A-tan B  1+ fan A. tan B cot(A+B)=cot A.cot B-1 cot A+cot B (h) cot(A-B)= cot A.cot B+1. cot B-cot A sin(A+B) (1) tan A+ tan B-- cos A.cos B +, Bzka) (j) cot A +cot B sin(B+A) sin A.sin B Yes Am. B ka+ (k) sin A+ sin B = 2 sin- A+B 2 A-B 2 .cos A+B A-B (1) sin A-sin B=2 cos-sin-2 (A+B)2 A-B (m) cos A+ cos B=2 cos A+B B-A (n) B B an B tan B cos A-cos B-2sin 2 (0) sin(A+B)+sin(A-B) = 2 sinA. cos B (p) sin(A+B)-sin(A-B)=2 cos A. sin B (q) cos(A+B)+cos(A-B)=2 cosA.cosB (1) 9. cos(A-B) cos(A+B)=2sinA.sinB Important formulas for multiple/sub-multiple of an angle (a) sin 2A 2 sin A.cos A = 1+tan² A 74 5 X.K. Publishers (b) 1-tan A cos 2A=cos A-sin A=- 1+tan A -2 cos A-1 1-2 s...

Many daily use products, not only beverages use Aspartame as a sugar alternative as it has zero calories and no bitter aftertaste like other sugar-free options. The Reuters report that Aspartame is going to be marked as a carcinogen has triggered health concerns. List of products that use Aspartame Diet Coke Coca-Cola Extra sugarfree Mars chewing gum Jell-O Sugarfree gelatin dessert mix Snapple zero sugar tea and juice drinks Sugar Twin 1 sweetener packets Equal zero calorie sweeteners Trident sugar-free peppermint gums What is a carcinogen? Carcinogens are substances that can cause cancer to humans. There are four levels of carcinogens: carcinogenic, probably carcinogenic, possibly carcinogenic and not classifiable. According to the Reuters report, Aspartame is likely to be classified as possibly carcinogenic -- the third category. What are other substances possibly carcinogenic? Carpentry Traditional Asian picked vegetables Occupational exposures in printing processes Occup...

in (  ENGLISH )  Your vision from sci-fi films is coming to reality as flying cars are all set to leap out of your imagination and onto the horizon. Yes, you read that right! A fully functional   electric car that you can drive on the roads as well as fly in the sky has just become the first flying car to receive legal approval to fly from the US  government. _________________ The flying car, developed by the US-based Alef Aeronautics, has received approval from the US government. The company announced that its car, known as Model A, has received the Special   Airworthiness Certification from the US Federal Aviation Administration (FAA). This development is historic as it marks the first time a vehicle of this kind has been certified in the US.----- 'The FAA is actively working on its policies for electrical vertical takeoff and landing (eVTOL) vehicles, as well as governing interactions between eVTOLs and ground infrastructure,' the company stated in ...

Fishy! JP Morgan accidentally deletes evidence in multi-million record retention screwup JP Morgan has been fined $4 million by America's securities watchdog, the SEC, for deleting millions of email records dating from 2018 relating to its Chase Bank subsidiary. The financial services giant apparently deleted somewhere in the region of 47 million electronic communications records from about 8,700 electronic mailboxes covering the period January 1 through to April 23, 2018. Many of these, it turns out, were business records that were required to be retained under the Securities Exchange Act of 1934, the SEC said in a filing detailing its findings. Worse still, the screwup meant that it couldn't produce evidence that that the SEC and others subpoenaed in their investigations. "In at least 12 civil securities-related regulatory investigations, eight of which were conducted by the Commission staff, JPMorgan received subpoenas and document requests for communications which coul...

नोटिफाई एक्ट, एक द्विदलीय विधेयक जो मंगलवार को प्रभावी होता है, चोरी, नकली या हानिकारक उत्पादों की बिक्री को रोकने के लिए ऑनलाइन मार्केटप्लेस को अपने विक्रेताओं की पहचान का खुलासा और सत्यापन करने की आवश्यकता होती है।   यह बिल तब आया जब खुदरा विक्रेताओं और व्यापार समूहों ने कांग्रेस में पैरवी की और खुदरा चोरी में वृद्धि के लिए ईबे और अमेज़ॅन जैसे ऑनलाइन बाज़ारों को दोषी ठहराया।   कानून का अनुपालन नहीं करने वाले ऑनलाइन बाज़ारों को प्रत्येक उल्लंघन के लिए $50,000 से अधिक जुर्माने का सामना करना पड़ सकता है। इन्फॉर्म एक्ट, एक नया कानून है जिसका उद्देश्य संगठित खुदरा चोरी और ऑनलाइन प्लेटफ़ॉर्म पर नकली और हानिकारक उत्पादों की बिक्री पर अंकुश लगाना है, मंगलवार से प्रभावी हो रहा है क्योंकि अधिक खुदरा विक्रेता कम मुनाफे के लिए चोरी को जिम्मेदार मानते हैं।  नए कानून में अमेज़ॅन और ईबे जैसे ऑनलाइन मार्केटप्लेस को तीसरे पक्ष के विक्रेताओं के बारे में जानकारी सत्यापित करने और साझा करने की आवश्यकता है जो बुरे कलाकारों को चोरी या हानिकारक सामान बेचने से रोकने के प्रयास में अपने प्लेटफॉर्...

News About Bitcoin  Bitcoin’s price has risen more than 12% since the beginning of June. Investors attributed the jump to news that BlackRock had filed for a spot bitcoin ETF. The more likely thing moving bitcoin, though, is large purchases by so-called bitcoin “whales” as liquidity remains low. This, analysts say, is causing big moves in the price of the world’s top digital currency. In pure ( Hindi )  इस महीने बिटकॉइन में तेजी से बढ़ोतरी हुई है - लेकिन उन कारणों से नहीं जिनके बारे में आप सोच सकते हैं।  दुनिया की सबसे बड़ी डिजिटल मुद्रा जून की शुरुआत से 12% से अधिक बढ़ी है।  कॉइन मेट्रिक्स डेटा के मुताबिक, बुधवार को इसकी कीमत 30,000 डॉलर के पार जाकर 14 अप्रैल के बाद के उच्चतम स्तर पर पहुंच गई।  बाजार के खिलाड़ियों ने इस उछाल के लिए इस खबर को जिम्मेदार ठहराया है कि अमेरिकी परिसंपत्ति प्रबंधन दिग्गज ब्लैकरॉक ने अंतर्निहित परिसंपत्ति के बाजार मूल्य पर नज़र रखने वाले स्पॉट बिटकॉइन एक्सचेंज-ट्रेडेड फंड के लिए आवेदन किया था।  हालांकि यह कारण का एक हि...

Apple's year-ahead product roadmap includes the new Apple   Watch Ultra with iPhone   15 this fall, according to a Bloomberg report. The company is also reportedly beginning work on a second-generation Vision Pro,   as well as a lower-end   model. Apple  is also expected to ship new M3-powered laptops,   and new OLED-screen iPads' will ship by next year,  per the   report. '

Explainer: How will Google BARD work, will it automatically write mail for you… Search experience will change  Google BARD Launch: A big change is going to happen in Google search soon.  The company has shown a glimpse of it in Google I / O 2023.  After the new change, your Google search experience will change a lot.  From here you will see AI Snapshot on searching about any topic.  In this, you will get a summary of the information related to your topic and many other details. In Google I / O 2023, the company has finally launched its AI chatbot BARD.  However, much more interesting than BARD is Google's new search, which can change the way you use the Internet.  Google is the most used search engine worldwide.  In such a situation, any change in its search methods will affect a large population.  In fact, earlier this year, Microsoft launched New Bing with ChatGPT of Search.  As soon as it came, many people started switchin...

School Closed: Holidays of all schools in Patna extended due to heat wave, know how long the schools will remain closed  In view of the scorching heat in Patna, the capital of Bihar, the holiday of all private and government schools from primary school, Anganwadi center to class 12th has been extended.  Now all the schools will remain closed till 28th June.  At the same time, on June 29, Bakrid is a government holiday. Humid summer is prevailing in Patna, the capital of Bihar.  Due to the scorching heat, the holidays of all schools in Patna district have been extended.  Patna's DM Dr. Chandrashekhar Singh has ordered to keep all government and non-government schools in the district closed for now.  According to the order, all schools up to class 12th will remain closed till June 28.  Earlier, the school was ordered to be closed from 19 to 24 June amid the scorching heat and heat wave. According to the order, in view of the scorc...

Vivo Y36 4G launched, 50MP camera and 5000mAh battery, the price is Rs.  Vivo Y36 4G Price in India: Vivo has launched its new smartphone in the Indian market.  This phone comes with powerful features.  In this you will get dual rear camera setup, whose main lens is 50MP.  Vivo has launched this phone in the mid range budget.  By the way, this phone comes with 4G support.  Let's know the price and other details of this phone Vivo has launched a new smartphone in its Y-series.  Vivo Y36 4G is a mid range phone.  However, 5G support has not been given in it.  This phone comes with Full HD display, Snapdragon processor, virtual RAM, big battery and super fast charging.  Dual rear camera setup has been given in the smartphone.  The handset has a 2.5D curved glass body.  It gets 8GB of RAM.  To give power to the device, a strong battery and 44W fast charging have been provided.  Let's know the price and other f...

Samsung Galaxy Z Flip 3 5G Offer: The cost of flip or folding phones sometimes prevents people from buying such phones.  But if you want, you can buy Samsung's flip phone cheaply. This smartphone is available on Flipkart at a very low price.  From here you will be able to buy this smartphone for less than 50 thousand rupees.  Let's know its details. If you want to buy a premium smartphone cheaply, then Samsung Galaxy Z Flip 3 is getting attractive offers.  This smartphone is currently available on Flipkart at almost half the price.  The company is selling it for less than Rs 50,000.  In this you get dual rear camera setup.  At the same time, the company has given a 10MP selfie camera in the front.  The smartphone works on the Qualcomm Snapdragon 888 processor, which is quite powerful.  In this you will get dual screen.  Let's know the price and other features of this smartphone. Samsung Galaxy Z Flip 3 5G price an...

 Now Who is the President of india Droupadi Murmu  ( née   Puti Biranchi Tudu ; born 20 June 1958) is an Indian politician and former teacher who is serving as the 15th and current  President of India  since 2022. She is the first person belonging to the  tribal  community and also the second woman after  Pratibha Patil  to hold the office. She is also the youngest person to occupy the post and the first President born in Independent India. She has also served as the 8th  Governor of Jharkhand  from 2015 to 2021. She has also previously served as a member of the  Odisha Legislative Assembly  from  Rairangpur Assembly constituency  from 2000 to 2009 and  Minister of State (Independent Charge) ,  Government of Odisha  from 2000 to 2004. Before entering politics, she worked as a clerk in the State Irrigation and Power Department from 1979 to 1983, and then as a teacher in ...

JK-QUIZ Indian Air Force 1. When and where was the Indian Air Force formed? Born on October 8, 1932 in present-day Pakistan. 2. What was the old name of Indian Air Force? Dr. Royal Indian Air Force. 3. When was the word Royal coined? J- 1945 during World War II. 4. When was the word Royal coined? A – On January 26, 1950 5.Why is the Air Force considered as a junior in India's defense? A – It consists of water and land forces. 6. Indian Air Force is divided into how many commands? of - 7 7. Where was the first Air Force Command formed? A - Karachi, No. 1 Smarjan. 8. Who was the first head of this warden number 1? A - Lt. C. A. Budjiar.

Jk-Quiz 6. India Quiz Temples and places of interest in India 1. Where are Ajanta and Ellora caves located? U- Maharashtra. Which religion is the temple associated with by Mount Act? Jainism. 3. What is the height of Kutbamin? ? A - 234 feet. What is the oldest bronze sculpture in India? R - Mahanjodaroga Nirju What is the name of the holy place of Jains? A - Samata (Bihar). What is the name of the holy place in India for Christians? R - Baba (Kerala) and Thomas (Matra) Kedarnath and Badrinath in which state and which deity is worshiped there do you sing A – Uttarakhand and Vishnu of Uttar Pradesh What is the name of the most powerful temple in India? - Tirupati Temple. 9. Where is the Nataraja Temple located? A - Tamil Nadu. 10. What is the name of the temple where Nataraj is worshipped? E – Vidambaram Temple. 11. Which temple in India worships rats? U - Kartidevi temple. 12. Kadevi temple is located in...

SWITCH TO DESKTOP SITE 9. 8- What are the names of the first 3 books printed in India? Conc Sous de Logica, Conc Sous De Philosophia o - 3. In which language were these 3 books published? A – Portuguese. 4. Doxina Christa was first translated into which Indian language? 8. 6. India Quiz Newspapers and Magazines of India 1. When was printing first established in India? A - 15556 years. Doctie or Christa. A – Konkani (1960s) When was the first Press Regulation Act? - 1799. What is the name of India's first newspaper? A - Bengal Gazette (1780). What was the other name of Bengal Gazette? 7. A - Calcutta General Adviser. Who was the publisher of Bengal Gazette? A – James Augustus Hickey. 8. What is the name of the first newspaper published in a regional language? A - News Mirror (Bengali) 9. 10. When was News Mirror published? A - 31 May 1818 11th. What is the name of India's oldest newspaper published till now? A – Mumbai News 12, When and who first publishe...

Who is President of America in 2023? :Joseph Robinette Biden Jr. (/ˈbaɪdən/ (listen) BY-dən; born November 20, 1942) is an American politician who is the 46th and current president of the United States. A member of the Democratic Party, he previously served as the 47th vice president from 2009 to 2017 under President Barack Obama and represented Delaware in the United States Senate from 1973 to 2009. Born in Scranton, Pennsylvania, Biden moved with his family to Delaware in 1953. He studied at the University of Delaware before earning his law degree from Syracuse University. He was elected to the New Castle County Council in 1970 and became the sixth-youngest senator in U.S. history after he was elected in 1972, at age 29. Biden was the chair or ranking member of the Senate Foreign Relations Committee for 12 years. He chaired the Senate Judiciary Committee from 1987 to 1995; drafted and led the effort to pass the Violent Crime Control and Law Enforcement Act and the Violence Against...

Adipurush (transl. First man)[a] is a 2023 Indian mythological action film based on the Hindu epic Ramayana.[6] The film is directed and co-written by Om Raut, and produced by T-Series and Retrophiles. Shot simultaneously in Hindi and Telugu, the film stars Prabhas, Saif Ali Khan, Kriti Sanon, Sunny Singh and Devdatta Nage. Adipurush was announced in August 2020, through an official motion poster. Principal photography commenced in February 2021 and ended in November 2021 taking place primarily in Mumbai. The film's music is composed by Ajay–Atul. Adipurush is budgeted at ₹500 crore (US$63 million) [7][3] making it the one of the most expensive Indian films. Adipurush was released on June 16, 2023 to negative reviews from critics, who praised the soundtrack and cast performances but criticised Raut's direction, screenplay, dialogues, visuals, and deviation from the source material. Adipurush film actors & actress ______ And writer 1.Kriti Sanon 2.Om Raut____ ...

Wikipedia is  a free, open-source online encyclopedia created and maintained by a community of volunteers, known as Wikipedians . 0  It operates under an open-source management style and is overseen by the nonprofit Wikimedia Foundation. The site uses a collaborative software called MediaWiki that facilitates the creation and development of articles.

  HOW CAN I USE  FREE DOMAIN NAME......? Unfortunately, it is not possible to get a domain for free. A domain is the address of your website and is issued by a domain registrar, which charges a fee for their services. However, there are ways to get a domain at a discounted price or with some additional perks, such as: 1. Special promotions from domain registrars - Some domain registrars offer limited-time promotions that allow you to get a domain name at a discounted price or for free with some conditions. 2. Free domain with web hosting - Some web hosting providers offer a free domain for the first year when you sign up for their hosting services. 3. Join a program that offers free domains - Some programs, such as Google's GSuite, offer free domains to their users. 4. Search for expired domains - You can search for expired domains, which means that the owner didn't renew the domain, and purchase them at a lower cost than a brand new domain. 5. Use a subdomain - If you don'...

Simple Interest Suppose, principal = . Rate of interest = R% and time = I So () Simple Interest (S.I.) = Principal × Interest Rate x Time PRT 100 100 100x (S.I.) 100 x simple interest (2) Principal (P) RxT Rate of interest x time 100 × (S.L.) 100) × simple interest (3) Rate of Interest (R) PXT Capital x time

Simple Interest Suppose, principal = . Rate of interest = R% and time = I So () Simple Interest (S.I.) = Principal × Interest Rate x Time PRT 100 100 100x (S.I.) 100 x simple interest (2) Principal (P) RxT Rate of interest x time 100 × (S.L.) 100) × simple interest (3) Rate of Interest (R) PXT Capital x time ________________________________

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