What is the general solution for cos^3(x)+cos(x)=0 ?

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

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cos^3(x)+cos(x)=0

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

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

Solution steps

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

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

sin (θ) = \frac{1}{3}, cos (θ) = \frac{2 2}{3}

sin (2 x) = \frac{3}{4}

sin (3 θ) - sin (5 θ) = sin (θ), 0 \leq θ \leq \frac{π}{2}

4 sin (2 θ) - 1 = 0

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

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