4.вычислите: cos(85°)+sin(125°)−cos(25°). 5.решите уравнение: −√3sin(x)−cos(x)=1. 6. решите уравнение: cos(8x)+cos(4x)+2sin^2(x)=1.

4
(cos85-cos25)+sin(180-55)=-2sin55sin30+sin55=-2*1/2*sin55+sin55=
=-sin55+sin55=0
5
-2(√3/2*sinx+1/2*cosx)=1
sinx*cosπ/6+cosx*sinπ/5=-1/2
sin(x+π/6)=-1/2
x+π/6=7π/6+2πn U x+π/6=11π/6+2πn
x=-π/6+7π/6+2πn U x=-π/6+11π/6+2πn
x=π+2πn U x=5π/3+2πn,n∈z
6
(cos8x+cos4x)+(2sin²x-1)=0
2cos6xcos2x+cos2x=0
cos2x*(2cos6x+1)=0
cos2x=0⇒2x=π/2+πn ⇒x=π/4+πn/2,n∈z
2cos6x+1=0⇒cos6x=-1/2⇒6x=+-2π/3+2πn⇒x=+-π/6+πn/3,n∈z