Question

Expand (a) cos(A-B+C)

Answer 1

Cos A - Cos B+ Cos C

Hope it will helpful

Answer 2

cos(A - B + C)

= cos((A - B) + C)

= cos(A - B).cosC - sin(A - B).sinC

= (cosA.cosB + sinA.sinB).cosC

- (sinA.cosB - cosA.sinB).sinC

= cosA.cosB.cosC + sinA.sinB.cosC

- sinA.cosB.sinC + cosA.sinB.sinC

Extra information:

$\boxed{\sf{sin(A+B) = sinA.cosB+cosA.sinB}}$

$\boxed{\sf{sin(A-B) = sinA.cosB-cosA.sinB}}$

$\boxed{\sf{cos(A+B) = cosA.cosB-sinA.sinB}}$

$\boxed{\sf{sin(A-B) = cosA.cosB+sinA.sinB}}$