Number of solutions of sqrt {tan theta } | vedclass

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Question

Let $	an 	heta=t \Rightarrow 	heta \in[0, \pi / 2] \cup\{\pi, 2 \pi\}$

$\Rightarrow \sqrt{t}=2 \sin 	heta$

squaring

$\left(1+\frac{1}{t^{

Vedclass · Accepted Answer

$5$

Vedclass · Answer

Let $	an 	heta=t \Rightarrow 	heta \in[0, \pi / 2] \cup\{\pi, 2 \pi\}$

$\Rightarrow \sqrt{t}=2 \sin 	heta$

squaring

$\left(1+\frac{1}{t^{2}}ight) t=4$

$\mathrm{t}+\frac{1}{\mathrm{t}}=4 \Rightarrow \mathrm{t}=2+\sqrt{3}, 2-\sqrt{3}$

$\Rightarrow 	heta=0, \frac{\pi}{12}, \frac{5 \pi}{12}, \pi, 2 \pi$

Number of solutions of $\sqrt {\tan \theta } = 2\sin \theta ,\theta \in \left[ {0,2\pi } \right]$ is equal to

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