What is the general solution for (cosX + sinX) (1 - 2sinX) = 0

1. square both sides, a straight forward method.

2. hand plot

3. calculator plot, not recommended. Let Y=sin x + cos x - 1

Y=0, find x=?

4. Substitute 1=sin^2 (x) + cos^2 (x) on the right hand side

Y1=sin^2 (x) - sin (x)

Y2=cos^2 (x) - cos (x)

Y1 + Y2=0, Y1=0, Y2=0,

a (a-1) = 0, so, a=0, a=1, where a=sin (x), or cos (x),

so x=0, pi/2

Have a good day!