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Prove that $(\sin 3x+\sin x)\sin x+(\cos 3x-\cos x)\cos x=0$

1 Answer

Toolbox:
  • $\cos A-\cos B=\cos A\cos B+\sin A\sin B$
  • $\cos^2A-\sin^2A=\cos 2A$
L.H.S
$(\sin 3x+\sin x)\sin x+(\cos 3x-\cos x)\cos x$
$\sin 3x.\sin x+\sin^2x+\cos 3x.\cos x-\cos^2x$
$\cos 3x.\cos x+\sin 3x.\sin x-(\cos^2x-\sin^2x)$
$\cos (3x-x)-\cos 2x$
$\cos 2x-\cos 2x=0$=R.H.S
Hence proved.
answered Apr 18, 2014 by sreemathi.v
 
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