Sin (5pi/2+2x) - 5 sin (3pi/2-x) - 1=0

Sin (2π+π/2+2x) - 5sin (3π/2-x) - 1=0

cos2x+5cosx-1=0

2cos²x-1+5cosx-1=0

cosx-a

2a²+5a-2=0

D=25-16=9

a1 = (-5-3) / 4=-2⇒cosx=-2<-1 нет решения

a2 = (-5+3) / 4=-1/2⇒cosx=-1/2⇒x=+-2π/3+2πn, n∈z