Question

Number of values of \( \theta \) lying in the interval \( (-\pi, \pi) \) such that \( \begin{vmatrix} \cos\theta & -\sin\theta & 1 \sin\theta & 1 & -\cos\theta 1 & \cos\theta & \sin\theta \end{vmatrix} = 2 \) is:

• A. 1
• B. 0
• C. 2
• D. 3

Hint:

Whenever you encounter the sum \( \sin^3\theta + \cos^3\theta \), substituting \( s = \sin\theta + \cos\theta \) often converts the trigonometric equation into a polynomial in \( s \). Always verify if the resulting roots fall within the range \( [-\sqrt{2}, \sqrt{2}] \).

Answer 1

The Correct Option is B