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Home  >>  CBSE XI  >>  Math  >>  Trigonometric Functions
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Evaluate $\sin x+\sin 3x+\sin 5x+\sin 7x$

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  • $\sin A+\sin B=2\sin \large\frac{A+B}{2}$$\cos \large\frac{A-B}{2}$
L.H.S
$\sin x+\sin 3x+\sin 5x+\sin 7x$
$\Rightarrow (\sin 7x+\sin x)+(\sin 5x+\sin 3x)$
$\Rightarrow 2\sin \large\frac{7x+x}{2}$$\cos \large\frac{7x-x}{2}$$+2\sin \large\frac{5x+3x}{2}$$\cos \large\frac{5x-3x}{2}$
$\Rightarrow 2\sin 4x\cos 3x+2\sin 4x\cos x$
$\Rightarrow 2\sin 4x(\cos 3x+\cos x)$
$\Rightarrow 2\sin 4x.2\cos \large\frac{3x+x}{2}$$\cos \large\frac{3x-x}{2}$
$\Rightarrow 4\sin 4x.\cos 2x.\cos x$
$\Rightarrow 4\cos x\cos 2x\sin 4x$=R.H.S
Hence proved.
answered Apr 18, 2014 by sreemathi.v
 

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