If cos (α+β) =0,  then, sin(α-β) can be reduced to

Correct option is D

Given:
cos(α + β) = 0

Identity Used:  

sin(90° - A) = cosA

cos(90° - A) = sinA
Solution:
From the trigonometric ratios,
 cos(α + β) = 0  

cos(α + β)  = cos90°

(α + β) = 90°

Now, α = 90° - β
Substitute the value of α,
sin(α - β) =sin(90° - β - β)
sin(α - β) = sin(90° -2β )    

                 = cos2β