If cosα + cosβ = A and sinα + sinβ = B, find sin(α – β)

If cosα + cosβ = A and sinα + sinβ = B, find sin(α – β).

(a) A²+B²-2/2

(b) A²+B²+2/2

(c) A² – B² + 1

(d) A² + B² – 4

Sol:

Put α = β = 0

A = 2

B = 0

Sin0 = 0

Only option D satisfies

(4) + 0 – 4 = 0