Question

If \( \cos x + \cos 2x = 1 \), then the value of \( \sin^{12}x + 3\sin^{10}x + 3\sin^8x + \sin^6x - 1 \) is equal to

• A. 2
• B. 1
• C. -1
• D. 0

Hint:

Use trigonometric identities to simplify expressions involving powers of sine and cosine.

Answer 1

The Correct Option is D

Step 1: Simplify the given trigonometric expression.
From the equation \( \cos x + \cos 2x = 1 \), we can express \( \cos 2x \) and solve for the values of \( \sin^2 x \). Substituting into the given polynomial expression, we get the value 0.

Step 2: Conclusion.
Thus, the correct answer is option (D).

Final Answer: \[ \boxed{\text{(D) 0}} \]