Question

prove that cot4x(sin5x+sin3x)= cotx(sin5x-sin3x)

Answer 1

hope this helps to u
if you get ur right answer and like my ans then plzzz mark as brainlist

Answer 2

LHS=
cot 4x( sin5x+sin 3x)=cot 4 x[2 sin(5x+3x/2)/cos (5x-3x/2)]
=cot 4x(2 sin4x.cos x)
=2 cos 4x/sin4x . sin 4x.cos x
=2cos 4x.cos x..(i)
RHS =
cot x(sin 5x-sin 3x)
=cot x [2 cos (5x+3x/2)sin(5x-3x/2)]
=cot x(2 cos 4x.sin x)
=2cos x /sin x.cos 4x.sinx
=2 cos x.cos 4x..(ii)
From eq (I) and (ii) LHS =RHS
[Formula sin a+sin b=2 sin(a+b/2).cos (a-b)] and sin a- sin b =2 cos (a+b/2).sin(a-b/2)]