Prove that: 2 ^23 4 +2 ^2 4 +2 ^2 3 =10 - Vidyadip

Question

Prove that: $2\sin^2\frac{3\pi}{4}+2\cos^2\frac{\pi}{4}+2\sec^2\frac{\pi}{3}=10$

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Answer

L.H.S =$2\sin^2\frac{3\pi}{4}+2\cos^2\frac{\pi}{4}+2\sec^2\frac{\pi}{3}$
$=2\Big\{\sin\Big(\pi-\frac{\pi}{4}\Big)\Big\}^2+2\Big(\frac{1}{\sqrt{2}}\Big)^2+2(2)^2$ $=2\Big\{\sin\frac{\pi}{4}\Big\}^2+2\times\frac{1}{2}+8$ $=2\Big(\frac{1}{\sqrt{2}}\Big)^2+1+8$ $=1+1+8$ $=10$ = R.H.S.

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