# Solve the equation if x is in (0,2pi) cos^2x+cosx-6=0

giorgiana1976 | College Teacher | (Level 3) Valedictorian

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We'll solve the trigonometric equation using substitution technique.

Let cos x = t

t^2 + t - 6 = 0

t1 = [-1+sqrt(1 + 24)]/2

t1 = (-1 + 5)/2

t1 = 2

t2 = (-1-5)/2

t2 = -3

But cos x = t

cos x = t1 <=> cos x = 2 impossible because the values of cosine function cannot be larger than 1.

cos x = t2 <=> cos x = -3 impossible because the values of cosine function cannot be smaller than -1.

Therefore, the given equation has no solution over the interval (0 , 2`pi` ).