Question

PROVE THAT sin11xsinx+sin7xsin3x divided by cos11xsinx+cos7xsin3x= tan 8x

Answer 1

The pic below helps u plz have a look at it

Answer 2

LHS = (sin11x. sinx +sin7x .sin3x)/(cos11x.sinx +cos7x.sin3x)

use formula ,

2sinA.sinB = cos(A-B)-cos(A+B)
2sinA.cosB =sin(A+B)+sin(A-B)

now,

=(cos10x -cos12x +cos4x -cos10x)/(sin12x- sin10x + sin10x -sin4x)

=(cos4x -cos12x)/(sin12x -sin4x)

=2sin8x.sin4x/2cos8x.sin4x

=tan4x = RHS