The solution of the equation cos^2theta, +, s | vedclass

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Question

$\cos ^{2} 	heta+\sin 	heta+1=0$

$\Rightarrow \quad 1-\sin ^{2} 	heta+\sin 	heta+1=0$

$\Rightarrow \quad \sin ^{2} 	heta-\sin 	heta-2=0$

Vedclass · Accepted Answer

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

Vedclass · Answer

$\cos ^{2} 	heta+\sin 	heta+1=0$

$\Rightarrow \quad 1-\sin ^{2} 	heta+\sin 	heta+1=0$

$\Rightarrow \quad \sin ^{2} 	heta-\sin 	heta-2=0$

$\Rightarrow \quad(\sin 	heta+1)(\sin 	heta-2)=0$

$\Rightarrow \quad \sin 	heta+1=0$

$[\because \sin 	heta-2=0 	ext { is not possible }]$

$\Rightarrow \quad \sin 	heta=-1$

$\Rightarrow \quad 	heta=\frac{3 \pi}{2} \in\left(\frac{5 \pi}{4}, \frac{7 \pi}{4}ight)$

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

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