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

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

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

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

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

Solution steps

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

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 (x) = 0.32

cos^{4} (x) + sin^{4} (x) = 1

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

sec^{2} (\frac{x}{2}) = 2

sec (θ) = - 3

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