Trig Question

[JohnCU]

Solve.

sin2xsinx - cos2xcosx = -cosx

Using double angle identities...

(2sinxcosx)sinx - (1-2sin^2x)cosx = -cosx
2sin^2xcosx - (cosx - 2sin^2xcosx) = -cosx
2sin^2xcosx - cosx + 2sin^2xcosx = -cosx

Add the cosx to the other side so they cancel...

2sin^2xcosx + 2sin^2xcosx = 4sin^2xcosx

Is this right? This was a quiz question and was marked wrong and I can't figure out what I'm doing wrong.

 

[imported_Mike]

are we solving, or proving an identity>?

 

[JohnCU]

The directions say "Solve, finding all solutions in [0, 2pi)."