Question

(sinx+siny)/(cosx+cosy)=tan (x+y)/2​

Answer 1

Answer:

Step-by-step explanation:

Given :

To prove :

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

Solution :

We know that,

$sin \ x \ + \ sin \ y = 2 \ sin \ \frac{x \ + \ y}{2} \ cos \ \frac{x \ - \ y}{2}$

&

$cos \ x \ + \ cos \ y = 2 \ cos \ \frac{x \ + \ y}{2} \ cos \ \frac{x \ - \ y}{2}$

So,

⇒ $\frac{sin \ x \ + \ sin \ y}{cos \ x \ + \ cos \ y} = \frac{2 \ sin \ \frac{x \ + \ y}{2} \ cos \ \frac{x \ - \ y}{2}}{2 \ cos \ \frac{x \ + \ y}{2} \ cos \ \frac{x \ - \ y}{2}}$

⇒ $(\frac{sin \ \frac{x \ + \ y}{2}}{cos \ \frac{x \ + \ y}{2}})(\frac{cos \ \frac{x \ - \ y}{2}}{cos \ \frac{x \ - \ y}{2}}) = tan \ \frac{(x \ + \ y)}{2}$