Question

Решите
4.sin3x/sinx=0

5.Cos4x/sin2x=sin4x/cos2x

Answer 1

4
sin3x=0 U sinx≠0
3x=πn⇒x=πn/3,n∈z U x≠πk,k∈z
x=πn/3,n∈z U n≠3k,k∈z
5
cos4x/sin2x-sin4x/cos2x=0
(cos4xcos2x-sin4xsin2x)/sin2xcos2x=0
2cos6x/sin4x=0
cos6x=0⇒6x=π/2+πn⇒x=π/12+πn/6,n∈z
sin4x≠0⇒4x≠πk⇒x≠πk/4.k∈z
x=π/12+πn/6,n∈z U n≠(3k-1)/2,k∈z

Answer 2

4
sin3x=0 U sinx≠0
3x=pin⇒x=pin/3,n∈z U x≠pik,k∈z
x=pin/3,n∈z U n≠3k,k∈z
5
cos4x/sin2x-sin4x/cos2x=0
(cos4xcos2x-sin4xsin2x)/sin2xcos2x=0
2cos6x/sin4x=0
cos6x=0⇒6x=pi/2+pin⇒x=pi/12+pin/6,n∈z 
sin4x≠0⇒4x≠pik⇒x≠pik/4.k∈z
x=pi/12+pin/6,n∈z U n≠(3k-1)/2,k∈z
pi-число пи (3,14)