The value of $\cos 20^{\circ}+2 \sin ^2 55^{\circ}-\sqrt{2} \sin 65^{\circ}$ is

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Aicharya · Accepted Answer

$\begin{aligned} & \cos 20^{\circ}+2 \sin ^2 55^{\circ}-\sqrt{2} \sin 65^{\circ} \ & =\cos 20^{\circ}+1-\cos 2\left(55^{\circ}ight)-\sqrt{2} \sin 65^{\circ} \ & \ldots\left[2 \sin ^2 	heta=1-\cos 2 	hetaight] \ & =\cos 20^{\circ}-\cos 110^{\circ}-\sqrt{2} \sin 65^{\circ}+1 \ & =2 \sin 65^{\circ} \sin 45^{\circ}-\sqrt{2} \sin 65^{\circ}+1 \ & =2 \sin 65^{\circ}\left(\frac{1}{\sqrt{2}}ight)-\sqrt{2} \sin 65^{\circ}+1 \ & =\sqrt{2} \sin 65^{\circ}-\sqrt{2} \sin 65^{\circ}+1 \ & =1\end{aligned}$

The value of $\cos 20^{\circ}+2 \sin ^2 55^{\circ}-\sqrt{2} \sin 65^{\circ}$ is

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