Hello! can anyone help me with a precalc problem?

Question

this question was on my quiz and i got it wrong, but im still not sure how to figure it out.

Solve in the interval 0 degrees less than or equal to "x" less than or equal to 360.

sin2xsinx - cos2xcosx = 1


thank you all very much!

Answer 1

Write this as:
cos2xcosx - sin2xsinx = -1
Recall the sum formula for the cosine:
cos(A + B) = cosAcosB - sinAsinB
Where A = 2x and B = x, your equation becomes:
cos(2x + x) = cos3x = -1
3x = 180
x = 60