Question:
If $\tan 3\theta = \cot \theta$, then $\theta =$
If $\tan 3\theta = \cot \theta$, then $\theta =$
Show Hint
Always convert mixed trigonometric equations (like tan and cot) into the same function before applying general solution formulas.
Updated On: May 14, 2026
- $\frac{(2n+1)\pi}{8}, n \in \mathbb{Z}$
- $\frac{(2n+1)\pi}{4}, n \in \mathbb{Z}$
- $\frac{(n+2)\pi}{3}, n \in \mathbb{Z}$
- $n\pi, n \in \mathbb{Z}$
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The Correct Option is A
Solution and Explanation
Step 1: Concept
Rewrite the equation in terms of tangent: $\tan 3\theta = \tan(\frac{\pi}{2} - \theta)$.
Step 2: Meaning
The general solution for $\tan \alpha = \tan \beta$ is $\alpha = n\pi + \beta$.
Step 3: Analysis
$3\theta = n\pi + (\frac{\pi}{2} - \theta)$. $4\theta = n\pi + \frac{\pi}{2} = \frac{2n\pi + \pi}{2} = \frac{(2n+1)\pi}{2}$. $\theta = \frac{(2n+1)\pi}{8}$.
Step 4: Conclusion
The general solution is $\theta = \frac{(2n+1)\pi}{8}$. Final Answer: (A)
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