If the equation cos ^{4} theta+sin ^{4} theta | vedclass

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Question

$\lambda=-\left(\sin ^{4} 	heta+\cos ^{4} 	hetaight)$

$\lambda=-\left(\sin ^{2} 	heta+\cos ^{2} 	hetaight)^{2}-2 \sin ^{2} 	heta \cos ^{2}

Vedclass · Accepted Answer

$\left[-1,-\frac{1}{2}\right]$

Vedclass · Answer

$\lambda=-\left(\sin ^{4} 	heta+\cos ^{4} 	hetaight)$

$\lambda=-\left(\sin ^{2} 	heta+\cos ^{2} 	hetaight)^{2}-2 \sin ^{2} 	heta \cos ^{2} 	heta$

$\lambda=\frac{\sin ^{2} 2 	heta}{2}-1$

$\lambda \in\left[-1,-\frac{1}{2}ight]$

$\frac{\sin ^{2} 2 	heta}{2} \in\left[0, \frac{1}{2}ight]$

If the equation $\cos ^{4} \theta+\sin ^{4} \theta+\lambda=0$ has real solutions for $\theta,$ then $\lambda$ lies in the interval

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