Please solve  sin x*cos x*cos 2x=-0.125*`sqrt 3`   for x.

Expert Answers
justaguide eNotes educator| Certified Educator

The equation `sin x*cos x*cos 2x = -0.125*sqrt 3` has to be solved for x.

`sin x*cos x*cos 2x = -0.125*sqrt 3`

=> `2*sin x*cos x*cos 2x = -0.25*sqrt 3`

=> `sin 2x*cos 2x = -0.25*sqrt 3`

=> `2*sin 2x*cos 2x = -0.5*sqrt 3`

=> `sin 4x = -0.5*sqrt 3`

`4x = sin^-1(-0.5*sqrt 3)`

=> `x = (sin^-1(-0.5*sqrt 3))/4`

=> `x = -15`

But the sine function is periodic with a period of 360 degrees.

The solution of the equation is -15 + n*360 degrees.