Question

Prove the following:-

$\frac{sin(x + y)}{sin(x - y)} = \frac{tan(x) + tan(y)}{tan(x) - tan(y)}$
​

Answer 1

LHS :

sin(x−y)

sin(x+y)

=

sinxcosy−cosxsiny

sinxcosy+cosxsiny

=

cosxcosy

sinxcosy−cosxsiny

cosxcosy

sinxcosy+cosxsiny

=

tanx−tany

tanx+tany

= RHS

Answer 2

Answer:

the above mentioned answer will help you.