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!
