Question

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

Answer 1

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