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Trigonometrical Equations
easy
$\cot \theta = \sin 2\theta (\theta \ne n\pi $, $n$ એ પૂર્ણાક છે.), જો $\theta = $
A
${45^o}$ અને ${60^o}$
B
${45^o}$ અને ${90^o}$
C
માત્ર ${45^o}$
D
માત્ર ${90^o}$
Solution
(b) $\cot \theta = \sin 2\theta ,{\rm{ }}(\theta \ne n\pi ) $
$\Rightarrow 2{\sin ^2}\theta \cos \theta = \cos \theta $
$ \Rightarrow $ $\cos \theta = 0$ or ${\sin ^2}\theta = \frac{1}{2} = {\sin ^2}\left( {\frac{\pi }{4}} \right)$
$ \Rightarrow $ $\theta = (2n + 1)\frac{\pi }{2}$ or $\theta = n\pi \pm \frac{\pi }{4}$
$ \Rightarrow $ $\theta = {90^o}$ and ${45^o}$.
Standard 11
Mathematics
