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Home  >>  CBSE XI  >>  Math  >>  Trigonometric Functions

Prove : $\sin 2x+2\sin 4x+\sin 6x=4\cos^2x\sin 4x$

1 Answer

Toolbox:
  • $\sin A+\sin B=2\sin \large\frac{A+B}{2}$$.\cos \large\frac{A-B}{2}$
  • $\cos 2x=2\cos^2x-1$
L.H.S
$\sin 2x+2\sin 4x+\sin 6x$
$\Rightarrow \sin 6x+\sin 2x+2\sin 4x$
$\Rightarrow 2\sin\large\frac{6x+2x}{2}$$.\cos \large\frac{6x-2x}{2}$$+2\sin 4x$
$\Rightarrow 2\sin 4x.\cos 2x+2\sin 4x$
$\Rightarrow 2\sin 4x(\cos 2x+1)$
$\cos 2x=2\cos^2x-1$
$\Rightarrow 2\sin 4x(2\cos ^2x-1+1)$
$\Rightarrow 4\sin 2x\cos^2x$=R.H.S
Hence proved.
answered Apr 17, 2014 by sreemathi.v
 
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