Question

решите уравнения
1)cos^2x - 1/2 =0
2)2cos x/9=1
3)tg(3x-P/4)=корень3
4)5sinx/3=корень40

Answer 1

6)(1+cos2x)/2=1/2
1+cos2x=1
cos2x=0
2x=π/2+πn,n∈Z
x=π/4+πn/2,n∈Z
7)cos(x/9)=1/2
x/9=+-π/3+2πn,n∈Z
x=+-3π+18πn,n∈Z
8)3x-π/4=π/3+πn,n∈Z
3x=7π/12+πn,n∈Z
x=7π/36+πn/3,n∈Z
9)sin(x/3)=√40/5>1 нет решения
10)сosx(8cosx-3)=0
сosx=0⇒x=π/2+πn,n∈Z
cosx=3/8⇒x=+-arccos3/8+πk,k∈Z