If 5cos 2theta + 2{cos ^2}frac{theta }{2} + 1 | vedclass

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Question

$5\cos 2	heta  + 2{\cos ^2}\frac{	heta }{2} + 1 = 0$

$ \Rightarrow $  $5(2{\cos ^2}	heta  - 1) + (1 + \cos 	heta ) + 1 = 0$

$

Vedclass · Accepted Answer

$\frac{\pi }{3},\pi - {\cos ^{ - 1}}\frac{3}{5}$

Vedclass · Answer

$5\cos 2	heta  + 2{\cos ^2}\frac{	heta }{2} + 1 = 0$

$ \Rightarrow $  $5(2{\cos ^2}	heta  - 1) + (1 + \cos 	heta ) + 1 = 0$

$ \Rightarrow $   $10{\cos ^2}	heta  + \cos 	heta  - 3 = 0$

$ \Rightarrow $   $(5\cos 	heta  + 3)\,(2\cos 	heta  - 1) = 0$

$ \Rightarrow $  $\cos 	heta  = \frac{1}{2},\,\cos 	heta  =  - \frac{3}{5}$

$\Rightarrow 	heta  = \frac{\pi }{3},\,\pi  - {\cos ^{ - 1}}\left( {\frac{3}{5}} ight)$.

If $5\cos 2\theta + 2{\cos ^2}\frac{\theta }{2} + 1 = 0, - \pi < \theta < \pi $, then $\theta = $

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