Cos(180+x)+sqrt3*cos(270+x)=2cos(90+2x) - вопрос №410996718032702902 от 123456789Ad1jssjsj 23.05.2023 20:56

Question

Алгебра: Cos(180+x)+sqrt3*cos(270+x)=2cos(90+2x)

123456789Ad1jssjsj · Answer

-cosx+√3sinx=-2sin2x2(√3/2sinx-1/2cosx)=2sin2xsin(x-π/6)=sin2xsin2x-sin(x-π/6)=02sin(x/2+π/12)cos(3x/2-π/12)=0sin(x/2+π/12)=0⇒x/2+π/12=πn⇒x/2=-π/12+πn⇒x=-π/6+2ππn,n∈Zcos(3x/2-π/12)=0⇒3x/2-π/12=π/2+πk⇒3x/2=7π/12+πk⇒x=7π/18+2πk/3,k∈Z...