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Trigonometrical Equations
medium
If $\tan \theta + \tan 2\theta + \sqrt 3 \tan \theta \tan 2\theta = \sqrt 3 ,$ then
A
$\theta = (6n + 1)\pi /18,\,\forall n \in I$
B
$\theta = (6n + 1)\pi /9,\,\forall n \in I$
C
$\theta = (3n + 1)\pi /9,\,\forall n \in I$
D
None of these
Solution
(c) Given relation is
$\tan \theta + \tan 2\theta + \sqrt 3 \tan \theta \tan 2\theta = \sqrt 3 $
==> $\,\tan \theta + \tan 2\theta = \sqrt 3 (1 – \tan \theta \tan 2\theta )$
==> $\frac{{\tan \theta + \tan 2\theta }}{{1 – \tan \theta \tan 2\theta }}$= $\sqrt 3 $
==> $\tan 3\theta = \tan (\pi /3)$
==> $3\theta = n\pi + \frac{\pi }{3}$
==> $\theta = (3n + 1)\frac{\pi }{9}$.
Standard 11
Mathematics
