What is the general solution for 4cos^2(x)-4cos(x)=-1 ?

The general solution for 4cos^2(x)-4cos(x)=-1 is x= pi/3+2pin,x=(5pi)/3+2pin

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4cos^2(x)-4cos(x)=-1

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

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

Solution steps

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

Solve by substitution

cos (x) = \frac{1}{2}

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

Combine all the solutions

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

2 sec (x) tan (x) = 0

tan^{2} (θ) - 3 tan (θ) - 4 = 0

3.25 = (9.8) sin (θ)

sin (θ) = - 3

sin (3 x - \frac{π}{3}) = \frac{1}{2}

What is the general solution for 4cos^2(x)-4cos(x)=-1 ?
The general solution for 4cos^2(x)-4cos(x)=-1 is x= pi/3+2pin,x=(5pi)/3+2pin