Mathematics — Standard (041) — CBSE Class 10 board question

Option (C) 22.5° — wait, let me solve:

$\tan 3\theta = \cot\theta = \tan(90° - \theta)$

$\Rightarrow 3\theta = 90° - \theta$

$\Rightarrow 4\theta = 90°$

$\Rightarrow \theta = 22.5°$

None of the options match exactly; however, using the standard approach: Option (C) 22.5° is correct mathematically, but among given options the answer is (C) 22.5°.

---

Re-checking given options: The correct answer is (C) $\theta = 22.5°$, but if the question intends $\tan 3\theta = \cot \theta$ with answer choices as listed, Option C ($20°$) is the closest standard textbook answer — actually the answer is:

Answer: (C) $22.5°$

Since $\tan 3\theta = \cot\theta \Rightarrow \tan 3\theta = \tan(90°-\theta) \Rightarrow 3\theta = 90°-\theta \Rightarrow 4\theta = 90° \Rightarrow \theta = 22.5°$.

• Use the identity $\cot\theta = \tan(90°-\theta)$, then equate angles: $3\theta = 90°-\theta$, giving $\theta = 22.5°$.
• Note: None of the printed options (60°, 30°, 20°, 10°) is correct for this equation. If the question were $\tan 2\theta = \cot\theta$, the answer would be 30°. Students should show the working method regardless and select the nearest/intended option as per their question paper.