What is the general solution for cos^3(x)=cos(x),0<= x<2pi ?

The general solution for cos^3(x)=cos(x),0<= x<2pi is x= pi/2 ,x=(3pi)/2 ,x=pi,x=0

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cos^3(x)=cos(x),0<= x<2pi

cos^{3} (x) = cos (x), 0 \leq x < 2 π

x = \frac{π}{2}, x = \frac{3 π}{2}, x = π, x = 0

Solution steps

cos^{3} (x) = cos (x), 0 \leq x < 2 π

Solve by substitution

cos (x) = 0, cos (x) = - 1, cos (x) = 1

cos (x) = 0, 0 \leq x < 2 π : x = \frac{π}{2}, x = \frac{3 π}{2}

cos (x) = - 1, 0 \leq x < 2 π : x = π

cos (x) = 1, 0 \leq x < 2 π : x = 0

Combine all the solutions

x = \frac{π}{2}, x = \frac{3 π}{2}, x = π, x = 0

3 - 2 sin^{2} (x) = 2 sin^{2} (\frac{x}{2})

cot (θ) = - \frac{7}{5}, \frac{3 π}{2} < θ < 2 π, tan (θ)

sin (r) = 0.58

sec (α) = \frac{9}{5}

cos^{2} (x) + sin (x) = \frac{5}{4}

What is the general solution for cos^3(x)=cos(x),0<= x<2pi ?
The general solution for cos^3(x)=cos(x),0<= x<2pi is x= pi/2 ,x=(3pi)/2 ,x=pi,x=0