If {sin ^2}theta - 2cos theta + frac{1}{4} = | vedclass

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Question

(b) $1 - {\cos ^2}	heta - 2\cos 	heta + \frac{1}{4} = 0$

$ \Rightarrow $ ${\cos ^2}	heta + 2\cos 	heta - \frac{5}{4} = 0$

$ \Rightarrow $ $\

Vedclass · Accepted Answer

$2n\pi \pm \frac{\pi }{3}$

Vedclass · Answer

(b) $1 - {\cos ^2}	heta - 2\cos 	heta + \frac{1}{4} = 0$

$ \Rightarrow $ ${\cos ^2}	heta + 2\cos 	heta - \frac{5}{4} = 0$

$ \Rightarrow $ $\cos 	heta = \frac{{ - 2 \pm \sqrt {4 + 5} }}{2} = - 1 \pm \frac{3}{2}$

Since $|\cos 	heta |\, \le 1$, 

hence $\cos 	heta = - 1 - \frac{3}{2}$ is ruled out.

$ \Rightarrow $ $\cos 	heta = - 1 + \frac{3}{2} = \frac{1}{2} = \cos \left( {\frac{\pi }{3}} ight)$

$ \Rightarrow $ $	heta = 2n\pi \pm \frac{\pi }{3}$.

If ${\sin ^2}\theta - 2\cos \theta + \frac{1}{4} = 0,$ then the general value of $\theta $ is

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