What is the general solution for 6cos^3(x)+cos^2(x)-1=0 ?

The general solution for 6cos^3(x)+cos^2(x)-1=0 is x= pi/3+2pin,x=(5pi)/3+2pin

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6cos^3(x)+cos^2(x)-1=0

6 cos^{3} (x) + cos^{2} (x) - 1 = 0

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Solution steps

6 cos^{3} (x) + cos^{2} (x) - 1 = 0

Solve by substitution

cos (x) = \frac{1}{2}, cos (x) = - \frac{1}{3} + i \frac{2}{3}, cos (x) = - \frac{1}{3} - i \frac{2}{3}

cos (x) = \frac{1}{2} : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

cos (x) = - \frac{1}{3} + i \frac{2}{3} :

No Solution

cos (x) = - \frac{1}{3} - i \frac{2}{3} :

No Solution

Combine all the solutions

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

4 tan^{2} (x) + 12 tan (x) - 27 = 0

sin^{2} (x) - cos (x) = \frac{1}{4}

cos^{4} (a) = 3 + 4 cos^{2} (a) + cos^{4} (a)

cos^{4} (t) = 1

8 cos^{2} (x) - 12 sin (x) - 12 = 0

What is the general solution for 6cos^3(x)+cos^2(x)-1=0 ?
The general solution for 6cos^3(x)+cos^2(x)-1=0 is x= pi/3+2pin,x=(5pi)/3+2pin