Question

Solve $\tan 2x = -\cot(x + \frac{\pi}{3})$

• A. $\frac{\pi}{6}$
• B. $n\pi + \frac{5\pi}{6}$
• C. $\frac{2\pi}{3}$
• D. None of these

Answer 1

Answer: (B)

$n\pi + \frac{5\pi}{6}$

Answer 2

Use the identity $-\cot \theta = \tan(\frac{\pi}{2} + \theta)$ to rewrite the equation as $\tan 2x = \tan(x + \frac{5\pi}{6})$. The general solution for $\tan A = \tan B$ is $A = n\pi + B$. Applying this, $2x = n\pi + x + \frac{5\pi}{6}$, which simplifies to $x = n\pi + \frac{5\pi}{6}$. This matches option (B).