Give method/reason. "If cos (α + β) = 0, then sin (α – β) can be reduced to:-"

(A) cos β
(B) cos 2β
(C) sin α
(D) sin 2α

α and ß are complementary, so  α = π/2 – ß, and α – ß = π/2 – 2ß

sin(π/2 – 2ß) = cos(2ß)

if cos(A + B) = 0 --> A + B = Pi /2 --> A = Pi/2 - B

sin(A - B) = sin(A)cos(B) - sin(B)cos(A)
= sin( Pi/2 - B - B)
= sin(Pi/2 - 2B) = sin(Pi/2)cos(2B) - sin(2B)cos(Pi/2)

sin(Pi/2) = 1 ; cos(Pi/2) = 0

Thus,
= (1)cos(2B) - sin(2B)(0)
= cos(2B)

Thus (B)

Hope this helps,

David