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

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

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

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

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

Solution steps

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

Solve by substitution

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

cos (x) = - 1 : x = π + 2 πn

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

Combine all the solutions

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

sin (3 x) = 0, 0 \leq x < 2 π

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

sin (θ) = - \frac{1}{5}, π < θ < \frac{3 π}{2}, cos (θ)

3 cot (θ) - 1 = 0, 0 \leq θ \leq 2 π

\frac{sin ( x )}{37} = \frac{sin ( 3 0 ^{\circ} )}{30}

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