General solution of tan 5θ = cot 2θ is ( where n ∈ Z )

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Trigonometrical Equations

easy

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

A

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

B

$\theta = \frac{{n\pi }}{7} + \frac{\pi }{5}$

C

$\theta = \frac{{n\pi }}{7} + \frac{\pi }{2}$

D

$\theta = \frac{{n\pi }}{7} + \frac{\pi }{3}$

Solution

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

Standard 11

Mathematics

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