solve trigonometric equation analytically for values of x for 0<=x<2pi

cos^2 x + 2 cos x + 1 = 0

We make a substitution cos x = t

t^2+2t+1=0

(t+1)^2=0

t+1=0

t=-1

So, cos x = -1

Since 0<=x<2pi, then x=pi

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