Question

решите уравнение 2cos^2x=1+sinx

Answer 1

2-2sin²x-1-sinx=0
2sin²x+sinx-1=0
sinx=a
2a²+a-1=0
D=1+8=9
a1=(-1-3)/4=-1⇒sinx=-1⇒x=-π/2+2πk,k∈z
a2=(-1+3)/4=1/2⇒sinx=1/2⇒x=π/6+2πk U x=5π/6+2πk,k∈z