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Trigonometrical Equations
medium
If $\tan 2\theta \tan \theta = 1$, then the general value of $\theta $ is
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
None of these
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
