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

1. 2sin 2α
2. 4
3. 4sin²α
4. -4sin²α

Correct answer: 4sin²α

Solution

The expression can be derived using the cosine of the angle difference identity and the properties of the cosine function. By substituting the values and simplifying, it can be shown that the result equals 4 times the square of the sine of the angle alpha, confirming option C as correct.

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