Cos (5 п/2-x) - 2cos2x=1

Cos (5 п/2-x) - 2cos2x=1

sinx-2cos2 x-1=0

sinx-2+4sin²x-1=0

sinx=a

4a²+a-3=0

D=1+48=49

a1 = (-1-7) / 8=-1⇒sinx=-1⇒x=-π/2+2πk, k∈z

a2 = (-1+7) / 8=3/4⇒sinx=3/4⇒x = (-1) ^karcsin3/4+πk, k∈z