Question

1. 4sin(x)*cos(x)-√2=0 2. 1-4sin(3x)*cos(3x)=0 3. cos(4x)*sin(3x)+cos(3x)*sin(4x)-1=0 4. sin^2(x)-3sin(x)+2=0 5. 4sin(x)+sin^-1(x)-4=0 6. cos^2(x)+1/2sin^4(x)-1=0

Answer 1

1)2sin2x=√2⇒sin2x=√2/2⇒2x=(-1)^n*π/4+πn⇒x=(-1)^n*π/8+πn/2
2)1-sin6x=0⇒sin6x=1⇒6x=π/2+2πn⇒x=π/12+πn/6
3)sin(3x+4x)=1
sin7x=1⇒7x=π/2+2πn⇒x=π/14+2πn/7
4)a=sinx
a²-3a+2=0, a1+a2=3 U a1*a2=2
a1=1⇒sinx=1⇒x=π/2+2πn
a2=2⇒sinx=2∉[-1;1]-нет решения
5)4sin²x-4sinx+1=0⇒(2sinx-1)²=0⇒2sinx=1⇒sinx=1/2⇒x=(-1)^n*π/6+πn
6)cos²x+1/2(1-cos²x)²-1=0
cos²x+1/2-cos²x+1/2cos^4x-1=0
1/2cos^4x-1/2=0
1/2(cos^4x-1)=0
(cos²x-1)(cos²x+1)=0
(cos²x+1)=0-нет решения
(cosx-1)(cosx+1)=0⇒cosx=1, x=2πn или cosx=-1,x=-π+2πn