important math formula

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 sin A

A(2n+1)

2 tan A tan 2A= 1-tan A

(c)

(d) (e) cos 3A =4 cos'A-3 cos A

sin 3A-3 sin A-4 sin A

3 tan A-4 tan'A (1) tan 3A =

1-3 tan A

A

D) (2)

4 tan A-4 tan A 1-6 tan A+ tan' A

tan 3A =

(h)

0 1-cos sin 8

tan-=

2 sin 0

1+cos

0 1+cose cot

2 sin 0

(1)

sin 0-3sin--4sin 3 3

(k)

0 cose = 4 cos -3 cos-3

3

3 Ꮎ 0 3 tan-tan 3 3

(1)

tan 0=

A 1-3 tan2 3

10.

(c) sin(A+B+C)=sin A.cos B.cosC+ cos A.sin B.cos C

+cos A. cos B. sin C-sinA. sinB.sinC

= cos A. cos B. cos C (tan AlanB + tan C. — tan A. tan

B. tanC)

Some formulae for compound angles (a) sin(A+B).sin(A-B)=sin A-sin B-cos B-cos A (b) cos(A+B).cos(A-B)-cos A-sin'B -cos B-sin'A

(d) cos(A+B+C) = cosA.cosB.coSC - sinA.sinB.cosC -

sinA.cosB.sinC-cosA.sinB.sinC

=cosA.cosB.cosC(1-tanA.tanB-tanB.tanC-tanC.tanA)

(e)

tan(A+B+C)

tanA+tanB+tanC-tanA.tanB.tanC 1-tanA.tanB-tanB.tanC-tanC.tanA

(0 con(A+B+C)

cotA.cosB.cotC-cotA-cotB-cotC

cotA.cotB+cotB.cotC+cotC.cotA-1

元

-0, +0,л+0,л-0,2-0,2+0 41 nida

2 2

Trigonometric Ratio Formula of Angles:

11.

(a) sin

(pl-0)=0

(b) cos(2-0)=si =sin 0

(c) tan ote (d) cot

(e) sin

= cos 0

=tan 0

=-sin e

ㅁ(+0) = CC

cot (2-0) = t (f) sin

76 8 S.K. Publishers

+0=-cot 0 tan

(g)

(h) sin(x-0)=sin 0

(i) соs(π-0)=-cos 0

(1)

tan(λ-0)=-tan 0

(k) sin(+0)=-sin 0

(1)

сos(л+0)=-cose

(n)

(c)

(m) tan(+0) = tan 0

sin(2-0)=-sin 0

(0)

cos(2π-0)= cos 0

(p) tan(2-0)=-tan 0

(q)

sin(2x+0)=sin0

(r) соs(2π+0) = cos 0

tan(2+0) = tan 0

(t)

sin(nλ+0)=(-1)" sin 0

(u)

cos(+0)=(-1)" cose

tan(+0) = tan 0

(w) sin(n-0)=(-1)" sine

(x) cos(m-0)=(-1)" cose

(y)

tan(n-0)=-tan 0

(zl)sin(2n+0)=sine

(v)

S

の

sin

sin 75

(22) cos (2n+0) = cose

(z3) tan (+0) = tan 0

-cot 0, if n is odd

(z4) tan

+0

tan 0, if n is even

(-1) cos 0, if n is odd 2

(z5)

sin

+0

(-1)2 cos 0, n is even

(-1)2 sine, if nis odd

(26) cos

PTIC

+0

(-1)2 cos 0, n is even