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

Question

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

Answer 1

-cosx+√3sinx=-2sin2x
2(√3/2sinx-1/2cosx)=2sin2x
sin(x-π/6)=sin2x
sin2x-sin(x-π/6)=0
2sin(x/2+π/12)cos(3x/2-π/12)=0
sin(x/2+π/12)=0⇒x/2+π/12=πn⇒x/2=-π/12+πn⇒x=-π/6+2ππn,n∈Z
cos(3x/2-π/12)=0⇒3x/2-π/12=π/2+πk⇒3x/2=7π/12+πk⇒x=7π/18+2πk/3,k∈Z

Comments

Огромное спасибо!!!Бесподобно!