If sin 2theta = cos theta ,,,0

Question

(d) $\sin 2	heta = \cos 	heta $

$\Rightarrow \cos 	heta = \cos \left( {\frac{\pi }{2} - 2	heta } ight)$

$ \Rightarrow $ $	heta = 2n\pi \p

Vedclass · Accepted Answer

${90^o},{30^o},{150^o}$

Vedclass · Answer

(d) $\sin 2	heta = \cos 	heta $

$\Rightarrow \cos 	heta = \cos \left( {\frac{\pi }{2} - 2	heta } ight)$

$ \Rightarrow $ $	heta = 2n\pi \pm \left( {\frac{\pi }{2} - 2	heta } ight) $

$\Rightarrow 	heta \pm 2	heta = 2n\pi \pm \frac{\pi }{2}$

$i.e.$, $3	heta = 2n\pi + \frac{\pi }{2} $

$\Rightarrow 	heta = \frac{1}{3}\left( {2n\pi + \frac{\pi }{2}} ight)$

and $ - 	heta = 2n\pi - \frac{\pi }{2}$

$\Rightarrow 	heta = - \left( {2n\pi - \frac{\pi }{2}} ight)$

Hence value of $	heta $ between $0$ and $\pi $ are $\frac{\pi }{6},\,\frac{\pi }{2},\,\frac{{5\pi }}{6}$

$i.e.$, ${30^o},\,{90^o},\,{150^o}$.

If $\sin 2\theta = \cos \theta ,\,\,0 < \theta < \pi $, then the possible values of $\theta $ are

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