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Home  >>  CBSE XI  >>  Math  >>  Trigonometric Functions
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Prove : $2\sin ^2\large\frac{3\pi}{4}$$+2\cos^2\large\frac{\pi}{4}$$+2\sec^2\large\frac{\pi}{3}$$=10$

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L.H.S
$2\sin^2(\pi-\large\frac{\pi}{4})$$+2(\cos\large\frac{\pi}{4})^2$$+2(\sec\large\frac{\pi}{3})^2$
$\Rightarrow 2(\sin\large\frac{\pi}{4})^2$$+2\times (\large\frac{1}{\sqrt 2})^2$$+2\times (2)^2$
$\Rightarrow 2\times (\large\frac{1}{\sqrt 2})^2$$+1+8=2\times \large\frac{1}{2}$$+1+8$
$\Rightarrow 1+1+8=10$=R.H.S
Hence proved.
answered Apr 17, 2014 by sreemathi.v
 

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