Question

solve for x cos^2x-sin^2x=sin x

Answer 1

Use the identity
(sinx)^2+(cosx)^2=1
or (cosx)^2=1-(sinx)^2
So:
1-(sinx)^2-(sinx)^2=sin(x)
1-2(sinx)^2=sin(x)
0=2(sinx)^2+sin(x)-1
sinx=[-1+sqrt(1+8)]/4 or [-1-sqrt(1+8)]/4
sinx=[-1+3]/4 or [-1-3]/4
sinx=2/4 or -4/4
sinx=1/2 or -1
If sinx=0.5
x=pi/6+2piK
or x=5pi/6+2piK
If sinx=-1
x=-pi/2+2piK
All the possible solutions are actually
x=pi/6+(2/3)piK
And -pi<x<=pi
The solutions are:
x= -pi/2, pi/6, 5pi/6