2sin^2px-cospx-1=0 (P- пи)

Question

2sin^2px-cospx-1=0
(P- пи)

Answer 1

2-2cos²πx-cosπx-1=0
2cos²πx+cosπx-1=0
cosπx=a
2a²+a-1=0
D=1+8=9
a1=(-1-3)/4=-1⇒cosπx=-1⇒πx=π+2πn⇒x=1+2n
a2=(-1+3)/4=1/2⇒cosπx=1/2⇒πx=+-π/3+2πn⇒x=+-1/3+2n