Решите

4. sin3x/sinx=0

5. Cos4x/sin2x=sin4x/cos2x

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+pi n/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)

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