Дам 50 балов, помогите решить)

Question

Дам 50 балов, помогите решить)

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Answer 1

1)4x=π/2+πn,n∈Z
x=π/8+πn/4,n∈Z
2)5x=-π/2+2πn,n∈Z
x=-π/10+πn/5,n∈Z
3)3x-1=πn,n∈Z
3x=1+πn,n∈Z
x=1/3+πn/3,n∈Z
4)2x+π/4=2πn,n∈Z
2x=-π/4+2πn,n∈Z
x=-π/8+πn,n∈Z
5)[sin3x+1=0⇒sin3x=-1⇒3x=-π/2+2πn,n∈∈Z⇒x=-π/6+2πn,n∈Z
[sinx/2-1=0⇒sinx/2=1⇒⇒x/2=π/2+2πk.k∈Z⇒x=π+4πk,k∈Z
6)[cos4x=0⇒4x=π/2+πn,n∈Z⇒⇒x=π/8+πn/4,n∈Z
[sinx/2=0⇒x/2=πk,k∈Z⇒x=2πk,k∈Z

Answer 2

1) cos4x=0
4x= π/2 + πn,  n∈Z
x= π + πn, n∈Z
     8     4

2) sin5x= -1
5x= -π/2+2πn,   n∈Z
x=  -π + 2πn,     n∈Z
      10      5

3) sin(3x-1)=0
3x-1=πn,         n∈Z
3x=1+πn,         n∈Z
x =  1  +  πn,    n∈Z
       3       3

4) cos(2x+ π/4)=1
2x+ π/4 =2πn,    π∈Z
2x=  -π/4 + 2πn
x= -π  + πn,   n∈Z
       8

5) (sin3x+1)(sin(x/2)-1)=0
1) sin3x+1=0
sin3x= -1
3x= -π/2 +2πn,  n∈Z
x= -π  +  2πn,    n∈Z
      6        3
2) sin(x/2)-1=0
sin(x/2)=1
x/2 = π/2 + 2πn,       n∈Z
x= π +4πn,   n∈Z

6) (cos4x)(sin(x/2))=0
1) cos4x=0
4x=π/2 + πn,  n∈Z
x=π  +  πn,   n∈Z
     8      4
2) sin(x/2)=0
x/2=πn,   n∈Z
x=2πn,    n∈Z