Question

sinx +siny =a, cosx +cosy =b find tan(x-y/2)

Answer 1

Hi ...dear...here is your answer..

... Given,
sinx +siny =a,
and
cosx +cosy =b....
...
..
we can apply the formula of cosC + cosD
and sinC + sinD....
let's start....

..see picture!!!
hope it helped you..
Regards Brainly Star Community
#shubhendu

Answer 2

Answer:

The value of $\tan(\frac{x+y}{2})=\frac{a}{b}$

Step-by-step explanation:

Given : $\sin x +\sin y =a, \cos x +\cos y =b$

To find : The value of $\tan(\frac{x+y}{2})$

Solution :

$\sin x +\sin y =a$

We know, $\sin x+\sin y=2\sin(\frac{x+y}{2})\cos(\frac{x-y}{2})$

$2\sin(\frac{x+y}{2})\cos(\frac{x-y}{2})=a$.....(1)

$\cos x +\cos y =b$

We know, $\cos x +\cos y =2\cos(\frac{x+y}{2})\cos(\frac{x-y}{2})$

$2\cos(\frac{x+y}{2})\cos(\frac{x-y}{2})=b$ ....(2)

Divide (1) and (2),

$\frac{2\sin(\frac{x+y}{2})\cos(\frac{x-y}{2})}{2\cos(\frac{x+y}{2})\cos(\frac{x-y}{2})}=\frac{a}{b}$

$\tan(\frac{x+y}{2})=\frac{a}{b}$

Therefore, The value of $\tan(\frac{x+y}{2})=\frac{a}{b}$