D5A8CA

sin2x+2sinx=√3cosx+√3

2sinxcosx+2sinx−√3cosx−√3=0

2sinx(cosx+1)−√3(cosx+1)=0

(cosx+1)(2sinx−√3)=0

1) cosx+1=0

cosx=-1

2)2sinx−√3=0

sinx = \frac{\sqrt{3}}{2}

x = \frac{ π }{3}+2 πl, l∈Ζ

x = \frac{2 π }{3} + 2 πn, n∈Ζ

x =  π+2 πk, k∈Ζ

[-3 π; - \frac{3 π }{2}]

-2 π+\frac{ π }{3}=-\frac{5 π }{3}

x = \frac{ π }{3}+2 πl, l∈Ζ

x = \frac{2 π }{3} + 2 πn, n∈Ζ

x =  π+2 πk, k∈Ζ

-\frac{5 π }{3}

-3 π