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

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

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

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

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

Solution steps

cos (x) + cos^{3} (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

- 2 cos (\frac{θ}{2}) = 0

cos (x) = - \frac{3}{4}, tan (x) i s

cos (θ) = \frac{- 1}{3}

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

- 2 sin^{2} (x) - 5 sin (x) = - 3

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