Question

Derive these identities using the addition or subtraction formulas for sine or cosine:

a. sin a sin b = 1 / 2(cos(a – b) – cos(a + b))

b. sin a cos b = 1 / 2(sin(a + b) + sin(a – b))

Answer 1

Explanation:

cos(a-b)-cos(a+b)=2(sina x sinb)

using formulae of cos (a-b) & cos(a+b)

cos a cos b + sina sinb - cosa cosb + sina sinb=2 sina sinb

2 sina sinb = 2 sina sinb

proved!