What is the general solution for cos^3(θ)=cos(θ) ?

The general solution for cos^3(θ)=cos(θ) is θ= pi/2+2pin,θ=(3pi)/2+2pin,θ=pi+2pin,θ=2pin

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cos^3(θ)=cos(θ)

cos^{3} (θ) = cos (θ)

θ = \frac{π}{2} + 2 πn, θ = \frac{3 π}{2} + 2 πn, θ = π + 2 πn, θ = 2 πn

Solution steps

cos^{3} (θ) = cos (θ)

Solve by substitution

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

cos (θ) = 0 : θ = \frac{π}{2} + 2 πn, θ = \frac{3 π}{2} + 2 πn

cos (θ) = - 1 : θ = π + 2 πn

cos (θ) = 1 : θ = 2 πn

Combine all the solutions

θ = \frac{π}{2} + 2 πn, θ = \frac{3 π}{2} + 2 πn, θ = π + 2 πn, θ = 2 πn

4 cos (2 x) = 22

4 sin^{4} (x) - 13 sin^{2} (x) + 3 = 0

3 tan (\frac{2 x}{3}) - 1 = 0

8 cos^{2} (θ) - 3 = 1

1 + 2 sin (x) = csc (x)

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