Question

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

Answer 1

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!