The sum of all values of theta , in ,lef | vedclass

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Question

${\sin ^2}2	heta \, + \,{\cos ^4}2	heta \, = \frac{3}{4}$

Let $\,{\cos ^2}2	heta \, =t $

$ \Rightarrow \,1\, - \,\,{\cos ^2}2	heta \, +

Vedclass · Accepted Answer

$\frac{{\pi }}{2}$

Vedclass · Answer

${\sin ^2}2	heta \, + \,{\cos ^4}2	heta \, = \frac{3}{4}$

Let $\,{\cos ^2}2	heta \, =t $

$ \Rightarrow \,1\, - \,\,{\cos ^2}2	heta \, + \,{\cos ^4}2	heta \, = \frac{3}{4}$

$ \Rightarrow t = \frac{1}{2}\, \Rightarrow \,\,{\cos ^2}2	heta \, = \frac{1}{2}\,$

$ \Rightarrow 2\,{\cos ^2}2	heta  - 1 = 0\, \Rightarrow \,\cos 4	heta \, = 0$

$ \Rightarrow \,4	heta \, = (2n + 1)\frac{\pi }{2}$

$ \Rightarrow \,	heta \, = (2n + 1)\frac{\pi }{8} \Rightarrow 	heta  = \frac{\pi }{8},\frac{{3\pi }}{8} \in \left[ {0,\frac{\pi }{2}} ight]$

Sum of values of $	heta $ is $\frac {\pi }{2}$

The sum of all values of $\theta \, \in \,\left( {0,\frac{\pi }{2}} \right)$ satisfying ${\sin ^2}\,2\theta + {\cos ^4}\,2\theta = \frac{3}{4}$ is

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