cos ^2 76^{circ}+sin ^2 46^{circ}+sin 76^{cir | vedclass

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(C) Let $E = \cos ^2 76^{\circ}+\sin ^2 46^{\circ}+\sin 76^{\circ} \cos 46^{\circ}$.Using the identity $2\cos^2 	heta = 1 + \cos 2	heta$ and $2\sin^

Vedclass · Accepted Answer

$\frac{5}{4}$

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(C) Let $E = \cos ^2 76^{\circ}+\sin ^2 46^{\circ}+\sin 76^{\circ} \cos 46^{\circ}$.Using the identity $2\cos^2 	heta = 1 + \cos 2	heta$ and $2\sin^2 	heta = 1 - \cos 2	heta$,we have:$E = \frac{1 + \cos 152^{\circ}}{2} + \frac{1 - \cos 92^{\circ}}{2} + \frac{1}{2} (2 \sin 76^{\circ} \cos 46^{\circ})$$E = 1 + \frac{1}{2} (\cos 152^{\circ} - \cos 92^{\circ}) + \frac{1}{2} (\sin(76^{\circ} + 46^{\circ}) + \sin(76^{\circ} - 46^{\circ}))$$E = 1 + \frac{1}{2} (-2 \sin 122^{\circ} \sin 30^{\circ}) + \frac{1}{2} (\sin 122^{\circ} + \sin 30^{\circ})$Since $\sin 30^{\circ} = \frac{1}{2}$,we get:$E = 1 - \frac{1}{2} \sin 122^{\circ} + \frac{1}{2} \sin 122^{\circ} + \frac{1}{4}$$E = 1 + \frac{1}{4} = \frac{5}{4}$.

$\cos ^2 76^{\circ}+\sin ^2 46^{\circ}+\sin 76^{\circ} \cos 46^{\circ} = $

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