Question

prove that sin(x+y)/sin(x-y)=tan(x)+tan(y)/tan(x)-tan(y)

Answer 1

HELLO THERE!

Let's see the Right Hand Side first.

We have,

$\frac{tan x + tan y}{tan x - tan y} \\\\= \frac{\frac{sinx}{cosx} + \frac{siny}{cosy}}{\frac{sinx}{cosx} - \frac{siny}{cosy}} \\\\= \frac{\frac{sinxcosy + cosxsiny}{cosxcosy}}{\frac{sinxcosy - cosxsiny}{cosxcosy}} \\\\= \frac{sinxcosy + cosxsiny}{sinxcosy - cosxsiny} \\\\= \frac{sin(x+y)}{sin(x-y)}$

Since,

sin(x + y) = sin x cos y + cos x sin y

and sin (x - y) = sin x cos y - cos x sin y.

HOPE THIS HELPS!

Thanks...