Question

If \( \theta = \frac{\pi}{9} \), then \( 1 + 27 \tan^2 \theta - 33 \tan^4 \theta + \tan^6 \theta = \)

• A. \( 3 \)
• B. \( \mathbf{4} \)
• C. \( -3 \)
• D. \( -11 \)

Hint:

Recognize symmetric polynomial identities and known angle values to evaluate directly.

Answer 1

The Correct Option is B

Let \( x = \tan \theta \). Given: \[ 1 + 27x^2 - 33x^4 + x^6 \] Use substitution: \( x = \tan \frac{\pi}{9} \). Now plug into the expression and simplify or use known identity evaluation: \[ \text{Expression evaluates to } 4 \]