Question

If \( \sin x + \sin^2 x = 1 \), then \( \cos^8 x + 2 \cos^6 x + \cos^4 x \) is

• A. 3
• B. 2
• C. 1
• D. 4

Hint:

When solving trigonometric expressions, simplify step-by-step and apply known identities such as \( \sin^2 x + \cos^2 x = 1 \).

Answer 1

The Correct Option is C

Step 1: Solve for \( \cos^2 x \).
From the given equation \( \sin x + \sin^2 x = 1 \), rearrange the terms: \[ \sin^2 x = 1 - \sin x \] Since \( \sin^2 x + \cos^2 x = 1 \), we substitute \( \sin^2 x = 1 - \sin x \) to find \( \cos^2 x \).
Step 2: Simplify the given expression.
The expression \( \cos^8 x + 2 \cos^6 x + \cos^4 x \) simplifies to 1 after evaluating.
Step 3: Conclusion.
Thus, the value of \( \cos^8 x + 2 \cos^6 x + \cos^4 x \) is \( 1 \).