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

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

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

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

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

Solution steps

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

Solve by substitution

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

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

cos (x) = i :

No Solution

cos (x) = - i :

No Solution

Combine all the solutions

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

csc (2 x) = 2 sin (2 x), 0 \leq x \leq 2 π

cos (x) = - \frac{12}{13}

x, z = arcsin (\frac{x}{y})

7 tan^{2} (θ) - 11 tan (θ) - 4 = - 8 tan (θ)

2 cos^{2} (2 θ) + sin (2 θ) = 1

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