General solution of 5 = 2 is ( where n Z ) - Vidyadip

MCQ

General solution of $\tan 5\theta = \cot 2\theta $ is $($ where $n \in Z )$

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

$ \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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