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Home  >>  CBSE XI  >>  Math  >>  Trigonometric Functions
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Prove : $\cos(\large\frac{3\pi}{4}$$+x)-\cos(\large\frac{3\pi}{4}$$-x)=-\sqrt 2\sin x$

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

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