The solution of equation {cos ^2}theta + sin | vedclass

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Question

(d) We have, ${\cos ^2}	heta + \sin 	heta + 1 = 0$

==> $1 - {\sin ^2}	heta + \sin 	heta + 1 = 0$

==> ${\sin ^2}	heta - \sin 	heta -

Vedclass · Accepted Answer

$\left( {\frac{{5\pi }}{4},\frac{{7\pi }}{4}} \right)$

Vedclass · Answer

(d) We have, ${\cos ^2}	heta + \sin 	heta + 1 = 0$

==> $1 - {\sin ^2}	heta + \sin 	heta + 1 = 0$

==> ${\sin ^2}	heta - \sin 	heta - 2 = 0$

==> $(\sin 	heta + 1)\,(\sin 	heta - 2) = 0$

$\sin 	heta = 2$, which is not possible and $\sin 	heta = - 1$.

Therefore, solution of given equation lies in the interval $\left( {\frac{{5\pi }}{4},\,\frac{{7\pi }}{4}} ight)$.

The solution of equation ${\cos ^2}\theta + \sin \theta + 1 = 0$ lies in the interval

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