Can you check if the question requires to solve for x or to prove the identity? I believe it is the latter.
Work on the right-hand-side:
cos(x)(4sin(x)-8sin³(x))
=4cos(x)sin(x)(1-2sin²(x))... factorization
=2sin(2x)(1-2sin²(x))... double angle formula
=2sin(2x)(1-2(1/2)(cos(0)-cos(2x)))... products formula
=2sin(2x)(1-1+cos(2x))
=2sin(2x)cos(2x)
=sin(4x) ... double angle formula
= left-hand-side
how to solve sin 4x= cosx(4 sinx - 8 sin ^3x)
4 answers
is to prove an identity
Done! :)
prove that cos thete + sec thete is equal 2 1