Trigonometry

Could someone help with the following question?
Solve thefollowing in the interval -180° to 180°.
sinx ( cosx + cosecx ) = 2cos^2 x

You don't have to give the solutions but just simplify the equation for me. I got as far as cos^2 x + sinxcosx - sin^2 x. I just want to eliminate either cos or sin from the equation

Could you post your working so far?

Could someone help with the following question?
Solve thefollowing in the interval -180° to 180°.
sinx ( cosx + cosecx ) = 2cos^2 x

You don't have to give the solutions but just simplify the equation for me. I got as far as cos^2 x + sinxcosx - sin^2 x. I just want to eliminate either cos or sin from the equation

Should have $-\cos^2 x + \sin x \cos x + \sin^2 x = 0$ instead.

Now just apply the double angle formulae?

Yeah sorry that's what I got. But how do i proceed further? Which double angle formula?

sin(2x) can be used on the middle term.

cos(2x) can be used on the two leftover terms.

Do you see it??

Yeah I totally do but I don't see how that would help me get my solutions for x..?

The point is that you use these to get an eqn in tan(2x)