Simplify the trigonometric expression: cos(2theta) + 2sin^2(theta).
Answer and explanation
Correct answer: D. 1
- Step 1: Use the double angle identity cos(2theta) = 1 - 2sin^2(theta).
- Step 2: Substitute into the expression: (1 - 2sin^2(theta)) + 2sin^2(theta) = 1.
Answer
1.
Why not the others: 'cos^2(theta)' applies only part of the identity cos(2theta) = cos^2(theta) - sin^2(theta); '2' adds coefficients erroneously; 'sin(2theta)' confuses addition with product.
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