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Trigonometrical Equations
medium
If $2\sin \theta + \tan \theta = 0$, then the general values of $\theta $ are
A
$2n\pi \pm \frac{\pi }{3}$
B
$n\pi ,2n\pi \pm \frac{{2\pi }}{3}$
C
$n\pi ,2n\pi \pm \frac{\pi }{3}$
D
$n\pi ,\,\,n\pi + \frac{{2\pi }}{3}$
Solution
(b) $2\sin \theta + \tan \theta = 0$; $\sin \theta \left( {2 + \frac{1}{{\cos \theta }}} \right) = 0$
$i.e.,$ $\sin \theta = 0 \Rightarrow \theta = n\pi $
or $\frac{1}{{\cos \theta }} = – 2 $
$\Rightarrow \cos \theta = – \frac{1}{2}$
$\Rightarrow \theta = 2n\pi \pm \left( {\frac{{2\pi }}{3}} \right)$.
Standard 11
Mathematics
