Trigonometrical Equations
medium

જો $\tan 2\theta \tan \theta = 1$, તો $\theta $ નો વ્યાપક ઉકેલ મેળવો.

A

$\left( {n + \frac{1}{2}} \right)\frac{\pi }{3}$

B

$\left( {n + \frac{1}{2}} \right)\,\pi $

C

$\left( {2n \pm \frac{1}{2}} \right)\frac{\pi }{3}$

D

એકપણ નહિ.

Solution

(a) $\tan 2\theta = \cot \theta $

==> $\tan 2\theta = \tan {\rm{ }}\left( {\frac{\pi }{2} – \theta } \right)$

$ \Rightarrow $ $2\theta = n\pi + \frac{\pi }{2} – \theta$

$\Rightarrow \theta = \frac{{n\pi }}{3} + \frac{\pi }{6}$.

Standard 11
Mathematics

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