Some formulae for compound angles

10.

(a)

(b)

(C)

Some formulae for compound angles

(e)

sin(A+B).sin(A-B) = sin'A-sin'B= cos'B-cos'A

cos(A+B).cos(A-B) = cos'A-sin'B = cos'B- sin'A

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

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

= cos A. cos B. cos C (tan AttanB + tan C- tan A. tan

B. tanC)

(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)

tan(A+B+C)

tanA+tanB+tanC-tanA.tanB.tanC

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

0 cot(A+B+C)

cotA.cosB.cotC- cotA -cotB-cotC

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