1)cos3x=√2÷2; 3x=arccos√2/2=+-π/4+2πn; n∈z; x=π/12+2πn/3; n∈z
2)x/2+π/4=-arctg1=-π/4+πn; n∈z; x=π+2πn; n∈z
3)2*sinx*cosx+cosx=0; cosx*(2sinx+1)=0; cosx=0; x=π/2+πn; n∈z
2sinx+1=0; sinx=-0.5; x=-arcsin0,5=-π/6+2πn; n∈z; x=7π/6+2πn; n∈z
4)cos7x+cosx=2cos((7x+x)/2)cos((7x-x)/2)=2cos4x*cos3x=0; cos4x=0; 4x=π/2+πn; n∈z; x=π/8+πn/4; n∈z; cos3x=0; 3x=π/2+πn; n∈z; x=π/6+πn/3; n∈z
5)2cos²x=1+cos2x=2-2sin²x; 2(1-sin²x+sinx)=2,5; 1-sin²x+sinx=1.25; sinx-sin²x=0.25; sinx-sin²x-0.25=0; -sin²x+sinx+0.25=0; sinx=t; -1≤t≤1; -t²+t+0.25=0; -4t²+4t+1=0; D=32;
(-4+4√2)/-8=(1-√2)/2; (-4-4√2)/-8=(1+√2)/2-посторонний корень; sinx=(1-√2)/2; x=arcsin((1-√2)/2)+2πn; n∈z