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Home  >>  CBSE XI  >>  Math  >>  Trigonometric Functions
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Prove $\large\frac{\sin x+\sin 3x}{\cos x+\cos 3x}$$=\tan 2x$

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Toolbox:
  • $\sin A+\sin B=2\sin \large\frac{A+B}{2}$$.\cos \large\frac{A-B}{2}$
  • $\cos A+\cos B=2\cos \large\frac{A+B}{2}$$.\cos \large\frac{A-B}{2}$
L.H.S
$\large\frac{\sin x+\sin 3x}{\cos x+\cos 3x}=\frac{\sin 3x+\sin x}{\cos 3x+\cos x}$
$\Rightarrow \large\frac{2\sin \Large\frac{3x+x}{2}\normalsize.\cos \Large\frac{3x-x}{2}}{2\cos \Large\frac{3x+x}{2}\normalsize.\cos \Large\frac{3x-x}{2}}$
$\Rightarrow \large\frac{\sin 2x}{\cos 2x}$
$\Rightarrow \tan 2x$=R.H.S
Hence proved.
answered Apr 17, 2014 by sreemathi.v
 

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