Trigonometric function and compound angle.

Prove that;

1. Tan5a+​​tan3a/tan5a-tan3a=sin8a/sin2a

To solve this equation you have to firstly convert tan in sin and cosin and then by taking LCM and using formula sin(a)cos(b)+cos(a)sin(b)  we can get the answer  i.e.

Tan5a = sin 5a / cos 5a

Tan3a= sin 3a / cos 3a

Putting values in equation and taking LCM we will get

[(sin 5a)(cos 3a) + (cos 5a)(sin 3a)]  / [(sin 5a)(cos 3a) - (cos 5a)(sin 3a)]

Now using formula