What is the general solution for 4cos^2(x)+4cos(x)-3=0 ?

The general solution for 4cos^2(x)+4cos(x)-3=0 is x= pi/3+2pin,x=(5pi)/3+2pin

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4cos^2(x)+4cos(x)-3=0

4 cos^{2} (x) + 4 cos (x) - 3 = 0

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

Solution steps

4 cos^{2} (x) + 4 cos (x) - 3 = 0

Solve by substitution

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

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

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

No Solution

Combine all the solutions

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

sin (4 x) cos (x) - cos (4 x) sin (x) = 0

2 sin (x) - (2 - 2) = 2 csc (x)

5 sin (62.83 x) = - 0.32

6 cos^{2} (θ) - 5 = 6 sin^{2} (θ) + sin (θ)

sin (\frac{1}{3} x) = 0

What is the general solution for 4cos^2(x)+4cos(x)-3=0 ?
The general solution for 4cos^2(x)+4cos(x)-3=0 is x= pi/3+2pin,x=(5pi)/3+2pin