The smallest positive angle which satisfies t | vedclass

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Question

$2 - 2{\cos ^2}	heta  + \sqrt 3 \cos 	heta  + 1 = 0$

$ \Rightarrow $  $2{\cos ^2}	heta  - \sqrt 3 \cos 	heta  - 3 = 0$

Vedclass · Accepted Answer

$\frac{{5\pi }}{6}$

Vedclass · Answer

$2 - 2{\cos ^2}	heta  + \sqrt 3 \cos 	heta  + 1 = 0$

$ \Rightarrow $  $2{\cos ^2}	heta  - \sqrt 3 \cos 	heta  - 3 = 0$

$ \Rightarrow $  $\cos 	heta  = \frac{{\sqrt 3  \pm \sqrt {3 + 24} }}{4} = \frac{{\sqrt 3 (1 \pm 3)}}{4} = \sqrt 3 \left( { - \frac{1}{2}} ight)$

$ \Rightarrow $  $	heta  = \frac{{5\pi }}{6}$.

The smallest positive angle which satisfies the equation $2{\sin ^2}\theta + \sqrt 3 \cos \theta + 1 = 0$, is

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