General solution of 5 = 2 is - Vidyadip

MCQ

General solution of $\tan 5 \theta=\cot 2 \theta$ is

✓
$\theta=\frac{n \pi}{7}+\frac{\pi}{14}$
B
$\theta=\frac{ n \pi}{7}+\frac{\pi}{5}$
C
$\theta=\frac{ n \pi}{7}+\frac{\pi}{2}$
D
$\theta=\frac{ n \pi}{7}+\frac{\pi}{3}$

✓

Answer

Correct option: A.

$\theta=\frac{n \pi}{7}+\frac{\pi}{14}$

(A) $\tan 5 \theta=\cot 2 \theta$
$\Rightarrow \tan 5 \theta=\tan \left(\frac{\pi}{2}-2 \theta\right)$
$\Rightarrow 5 \theta= n \pi+\frac{\pi}{2}-2 \theta$
$\Rightarrow 7 \theta= n \pi+\frac{\pi}{2}$
$\Rightarrow \theta=\frac{ n \pi}{7}+\frac{\pi}{14}$

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