Question

Determinati x apartine (0,pi), stiind ca sin 2x-3 sin x-2 cos x+3=0

Answer 1

sin2x - 3sinx-2cosx+3=0

2sinx*cosx-3sinx-2cosx+3=0

2cosx(sinx-1)-3(sinx-1)=0

(sinx-1)(2cosx-3)=0

cosx=3/2 =>x€ multime vida

sinx=1=>x=pi/2 +2kpi

dar x€(0,pi)=>x=pi/2

R: S={pi/2}

Bafta!