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

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

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