The number of values of theta in the interval | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

$ 	an 	heta=\cot 5 	heta $

$ \Rightarrow \cos 6 	heta=0 $

$ 4 \cos ^3 2 	heta-3 \cos 2 	heta=0 $

$ \Rightarrow \cos 2 	heta=0 	ext {

Vedclass · Accepted Answer

$3$

Vedclass · Answer

$ 	an 	heta=\cot 5 	heta $

$ \Rightarrow \cos 6 	heta=0 $

$ 4 \cos ^3 2 	heta-3 \cos 2 	heta=0 $

$ \Rightarrow \cos 2 	heta=0 	ext { or } \pm \frac{\sqrt{3}}{2} $

$ \sin 2 	heta=\cos 4 	heta $

$ \Rightarrow 2 \sin ^2 2 	heta+\sin 2 	heta-1=0 $

$ 2 \sin ^2 2 	heta+2 \sin 2 	heta-\sin 2 	heta-1=0 $

$ \sin 2 	heta=-1 	ext { or } \sin 2 	heta=\frac{1}{2} $

$ \cos 2 	heta=0 	ext { and } \sin 2 	heta=-1 $

$ \Rightarrow 2 	heta=-\frac{\pi}{2} \Rightarrow 	heta=-\frac{\pi}{4} $

$ \cos 2 	heta= \pm \frac{\sqrt{3}}{2}, \sin 2 	heta=\frac{1}{2} $

$ \Rightarrow 2 	heta=\frac{\pi}{6}, \frac{5 \pi}{6} \Rightarrow 	heta=\frac{\pi}{12}, \frac{5 \pi}{12} $

$ 	herefore 	heta=-\frac{\pi}{4}, \frac{\pi}{12}, \frac{5 \pi}{12}$

The number of values of $\theta$ in the interval $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$ such that $\theta \neq \frac{n \pi}{5}$ for $n=0, \pm 1, \pm 2$ and $\tan \theta=\cot 5 \theta$ as well as $\sin 2 \theta=\cos 4 \theta$ is

Similar Questions

If $\tan (\pi \cos \theta ) = \cot (\pi \sin \theta ),$ then the value of $\cos \left( {\theta - \frac{\pi }{4}} \right) =$

If $\alpha ,\,\beta ,\,\gamma $ and $\delta $ are the solutions of the equation $\tan \left( {\theta + \frac{\pi }{4}} \right) = 3\,\tan \,3\theta $ , no two of which have equal tangents, then the value of $tan\, \alpha + tan\, \beta + tan\, \gamma + tan\, \delta $ is

Number of solution$(s)$ of the equation $\sin 2\theta + \cos 2\theta = - \frac{1}{2},\theta \in \left( {0,\frac{\pi }{2}} \right)$ is-

General solution of $\tan 5\theta = \cot 2\theta $ is $($ where $n \in Z )$

The general value of $\theta $ that satisfies both the equations $cot^3\theta + 3 \sqrt 3 $ = $0$ & $cosec^5\theta + 32$ = $0$ is $(n \in I)$