Substituting the values of \( sin\dfrac{3\pi}{4},cos \dfrac{\pi}{4},sec\dfrac{\pi}{3}\) on left hand side,
L.H.S.= \( 2 sin^2\dfrac{3\pi}{4}+2cos^2\dfrac{\pi}{4}+2sec^2\dfrac{\pi}{3}\)
\(2\{sin(\pi-\dfrac{\pi}{4})\}^2+2(\dfrac{1}{\sqrt{2}})^2+2(2)^2\)
\( 2\{sin\dfrac{\pi}{4}\}^2+2\times \dfrac{1}{2}+8\)
Since sinx repeat its value after interval of 2π
We have, \( sin\dfrac{3\pi}{4}= sin\dfrac{\pi}{4}\)
L.H.S 1 +1+ 8
=10 = R.H.S.
Hence proved.
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