Question

If cos⁻1x-cos⁻1(y)/(2)=α, then 4x²-4xycosα+y² is equal to

• A. \(2\sin 2\alpha\)
• B. \(4\)
• C. \(4\sin^2\alpha\)
• D. 4-4sin²α

Hint:

Use trigonometric identities to reduce algebraic expressions.

Answer 1

The Correct Option is C

Using cosine difference identity and simplifying, 4x²-4xycosα+y²=(2x-y)²+4xysin²α Hence the expression reduces to: 4sin²α