If cos(A - α) = p, sin(A - β) = q, then the value of cos²(α - β) + 2pqsin(α - β) is:

A. 4p²q²

B. p² - q²

C. p² + q²

D. p²q²

Answer: Option C

Solution(By Examveda Team)

cos(A - α) = p, sin(A - β) = q
Here, two equation, and four variable,
So, α = β = 0,
cosA = p, sinA = q
Now, cos²(α - β) + 2pq sin(α - β)
cos²0 + 2pq × sin0
1 + 0 = 1
By option, (C) = p² + q²
= cos²A + sin²A
= 1