Question 944798
find all solutions of the equation on the interval [0, 2pie). - square root 3 cos x + sin x = -square root 3
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{{{sqrt(3)cosx+sinx=-sqrt(3)}}}
{{{sqrt(3)cosx+sqrt(3)=-sinx}}}
{{{sqrt(3)(cosx+1)=-sinx}}}
square both sides:
3(cos^2(x)+2cosx+1)=sin^2(x)
3cos^2(x)+6cosx+3=1-cos^2(x)
4cos^2(x)+6cosx+2=0
2cos^2(x)+3cosx+1=0
(2cosx+1)(cosx+1)=0
..
2cosx+1=0
cosx=-1/2
x=2π/3, 4π/3
..
cosx+1=0
cosx=-1
x=π