Question

Find the points of the curve at which the tangent line to the function y=(cosx)/(2+sinx) is horizontal. I think i've mostly figured the problem out.

Answer 1

Ok i know the derivative equal to 0 will give me my answer if i solve for x. So first I did quotient rule

Answer 2

and got \[\frac{ (-sinx)(2+sinx)-(cosx)(cosx) }{ (2+sinx)^2 }\]

Answer 3

I then simplified and got \[-2sinx-\sin^2x-\cos^2x=0\]

Answer 4

I just don't know how to solve for x from this