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Prove :$\large\frac{\sin 5x+\sin 3x}{\cos 5x+\cos 3x}$$=\tan 4x$

1 Answer

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}$
$\large\frac{\sin 5x+\sin 3x}{\cos 5x+\cos 3x}$
$\Rightarrow \large\frac{2\sin \Large\frac{5x+3x}{2}.\cos \Large\frac{5x-3x}{2}}{2\cos \Large\frac{5x+3x}{2}.\cos \Large\frac{5x-3x}{2}}$
$\Rightarrow \large\frac{\sin 4x.\cos x}{\cos 4x.\cos x}=\frac{\sin 4x}{\cos 4x}$
$\Rightarrow \tan 4x$=R.H.S
Hence proved.
answered Apr 17, 2014 by sreemathi.v
 
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