Question

(sin A + sin B)/ (cos A+ cos B)= tan (A+B/2) JO PROVE KARE POINTS USKE​

Answer 1

Step-by-step explanation:

We have,

$\frac{\sin(A) + \sin(B)}{\cos(A) + \cos(B)} = \frac{2\sin( \frac{A + B}{2}) \cos(\frac{A - B}{2}) }{2\cos(\frac{A + B}{2}) \cos(\frac{A - B}{2})}$

$\implies \: \frac{\sin(A) + \sin(B)}{\cos(A) + \cos(B)} = \frac{\sin( \frac{A + B}{2}) }{ \cos(\frac{A + B}{2})}$

$\implies \: \frac{\sin(A) + \sin(B)}{\cos(A) + \cos(B)} =\tan \bigg( \frac{A + B}{2} \bigg)$