The number of elements in the set S =left{the | vedclass

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Sol. $3 \cos ^4 	heta-5 \cos ^2 	heta-2 \sin ^6 	heta+2=0$

$\Rightarrow \quad 3 \cos ^4 	heta-3 \cos ^2 	heta-2 \cos ^2 	heta-2 \sin ^6 	het

Vedclass · Accepted Answer

$9$

Vedclass · Answer

Sol. $3 \cos ^4 	heta-5 \cos ^2 	heta-2 \sin ^6 	heta+2=0$

$\Rightarrow \quad 3 \cos ^4 	heta-3 \cos ^2 	heta-2 \cos ^2 	heta-2 \sin ^6 	heta+2=0$

$\Rightarrow \quad 3 \cos ^4 	heta-3 \cos ^2 	heta+2 \sin ^2 	heta-2 \sin ^6 	heta=0$

$\Rightarrow \quad 3 \cos ^2 	heta\left(\cos ^2 	heta-1ight)+2 \sin ^2 	heta\left(\sin ^4 	heta-1ight)=0$

$\Rightarrow \quad-3 \cos ^2 	heta \sin ^2 	heta+2 \sin ^2 	heta\left(1+\sin ^2 	hetaight) \cos ^2 	heta-1$

$\Rightarrow \quad \sin ^2 	heta \cos ^2 	heta\left(2+2 \sin ^2 	heta-3ight)=0$

$\Rightarrow \quad \sin ^2 	heta \cos ^2 	heta\left(2 \sin ^2 	heta-1ight)=0$

$(C1)$ $\sin ^2 	heta=0 ightarrow 3$ solution ; $	heta=\{0, \pi, 2 \pi\}$

$(C2)$ $\cos ^2 	heta=0 ightarrow 2$ solution $; 	heta=\left\{\frac{\pi}{2}, \frac{3 \pi}{2}ight\}$

(C) $\sin ^2 	heta=\frac{1}{2} ightarrow 4$ solution; $	heta=\left\{\frac{\pi}{4}, \frac{3 \pi}{4}, \frac{5 \pi}{4}, \frac{7 \pi}{4}ight\}$

No. of solution $=9$

The number of elements in the set $S =\left\{\theta \in[0,2 \pi]: 3 \cos ^4 \theta-5 \cos ^2 \theta-2 \sin ^2 \theta+2=0\right\}$ is $...........$.

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