Question

For \( \theta \in \left( 0, \frac{\pi}{2} \right) \), if \( \tan 3\theta \cdot \tan 2\theta \cdot \tan \theta + \tan 2\theta + \tan \theta = 1 \), then \( \theta = \)

• A. \( \frac{\pi}{12} \)
• B. \( \frac{\pi}{4} \)
• C. \( \frac{\pi}{6} \)
• D. \( \frac{\pi}{3} \)

Hint:

For trigonometric equations, simplify step-by-step and use known identities to solve for the variable.

Answer 1

The Correct Option is A

Step 1: Use the given equation.
We are given the equation: \[ \tan 3\theta \cdot \tan 2\theta \cdot \tan \theta + \tan 2\theta + \tan \theta = 1 \] By solving the equation, we find that \( \theta = \frac{\pi}{12} \).
Step 2: Conclusion.
Thus, the value of \( \theta \) is \( \frac{\pi}{12} \), corresponding to option (A).