If $ heta$ is in the interval $\left(0, \frac{\pi}{2} ight)$ satisfying the equation $\cos 2 heta \cdot \sec ^4 heta+\sec ^2 heta=0$, then $\sin ^2 heta=$

Question

If $	heta$ is in the interval $\left(0, \frac{\pi}{2}ight)$ satisfying the equation $\cos 2 	heta \cdot \sec ^4 	heta+\sec ^2 	heta=0$, then $\sin ^2 	heta=$

Aicharya · Accepted Answer

$\begin{array}{lrl}	ext {Given, } \cos 2 	heta \cdot \sec ^4 	heta+\sec ^2 	heta=0, 	heta \in(0, \pi / 2) \ \Rightarrow & \left(1-	an ^2 	hetaight) \sec ^2 	heta+\sec ^2 	heta=0 \ \Rightarrow & \sec ^2 	heta\left[1-	an ^2 	heta+1ight]=0 \ \Rightarrow & 	an ^2 	heta=2 \ \Rightarrow & \sin ^2 	heta=2 / 3\end{array}$

If $\theta$ is in the interval $\left(0, \frac{\pi}{2}\right)$ satisfying the equation $\cos 2 \theta \cdot…

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