sedinalana 3)
8*sinx*cos2x*cosx=√3
4*2*sinx*cosx*cos2x=√3
4*sin2x*cos2x=√3
2*2*sin2x*cos2x=√3
2*sin4x=√3
sin4x=√3/2
4x=π/3+2πn    x₁=π/12+πn/2
4x=2π/3+2πn  x₂=π/6+πn/2.
4) 4sinx*cosx*cos2x=cos4x
2*2sinx*cosx*cos2x=cos4x
2*sin2*cos2x=cos4x
sin4x=cos4x  |÷cos4x
tg4x=1
4x=π/4+2πn     x₁=π/16+πn/2
4x=5π/4+2πn   x₂=5π/16+πn/2.

sangers1959

Verified answer

3
8sinx*cosx*cos2x=√3
4sin2x*cos2x=√3
2sin4x=√3
sin4x=√3/2
4x=π/3+2πk⇒x=π/12+πk/2,k∈z
4x=2π/3+2πk⇒x=π/6+πk/2,k∈z
4
4sinxcosx*cos2x=cos4x
2sin2x*cos2x=cos4x
sin4x-cos4x=0
sin4x-sin(π/2-4x)=0
2SIn(4x-π/4)cosπ/4=0
2*√2/2*sin(4x-π/4)=0
sin(4x-π/4)=0
4x-π/4=πk,k∈z
4x=π/4+πk,k∈z
x=π/16+πk/4,k∈z