Question

(2 tan 5theta+ tan 3theta)/
(tan 5theta-tan 3theta) =
4 cos 2theta *cos 4theta​

Answer 1

Step-by-step explanation:

(tan 5x+tan 3x)/(tan 5x -tan 3x) = 4 cos 2x cos 4x.

L.H.S .

=(sin 5x /cos 5x +sin 3x /cos 3x)/( sin 5x / cos 5x - sin 3x/ cos 3x).

=[(sin 5x.cos 3x+cos 5x.sin 3x)/cos 5x.cos 3x]/[(sin 5x.cos 3x -cos 5x.sin 3x)/cos 5x.cos 3x]

=sin(5x+3x)/sin (5x-3x).

=sin8x/sin2x.

=2sin4x.cos 4x/sin 2x.

=2.2sin 2x.cos 2x.cos 4x/sin2x.

=4cos 2x.cos 4x. , Proved.