Question

(1-cosx+sinx)/(1+cosx+sinx)=tan(x/2)​

Answer 1

The solution is in the attachment

Hope it helps you

Thank you

Answer 2

Answer:

■ Here we prove

LHS = RHS

$\frac{(1 - \cos \: x + \sin \: x) }{(1 + \cos \: x + \sin \: x) } \\ \\ = \frac{(2 \: { \sin \: }^{2} \frac{x}{2} + 2 \sin \: \frac{x}{2} \cos \: \frac{x}{2} )}{(2 \: { \sin \: }^{2} \frac{x}{2} +2 \sin \: \frac{x}{2} \cos \: \frac{x}{2} )}$

now ,

separate a common , we get

$= \frac{ 2\sin \: \frac{x}{2} \: \: ( \sin \: \frac{x}{2} + \cos \: \frac{x}{2} )}{2\cos \: \frac{x}{2} \: \: ( \cos \: \frac{x}{2} + \sin \: \frac{x}{2} )} \\ \\ = \frac{ \sin \: \frac{x}{2} ( \sin \: \frac{x}{2} + \cos \: \frac{x}{2} ) }{\cos \: \frac{x}{2} ( \sin \: \frac{x}{2} + \cos \: \frac{x}{2} )} \\ \\ = \frac{ \sin \: \frac{x}{2} }{ \cos \: \frac{x}{2} } \\ \\ = \tan \: \frac{x}{2}$

LHS = RHS

hope it helps....

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