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

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

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cos(x)+cos^2(x)+cos^3(x)=0

cos (x) + cos^{2} (x) + cos^{3} (x) = 0

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

Solution steps

cos (x) + cos^{2} (x) + cos^{3} (x) = 0

Solve by substitution

cos (x) = 0, cos (x) = - \frac{1}{2} + i \frac{3}{2}, cos (x) = - \frac{1}{2} - i \frac{3}{2}

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

cos (x) = - \frac{1}{2} + i \frac{3}{2} :

No Solution

cos (x) = - \frac{1}{2} - i \frac{3}{2} :

No Solution

Combine all the solutions

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

cos (x) - sin (x) = \frac{1}{( sin ( x ) )} - \frac{1}{( cos ( x ) )}

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

16 = 4 + 9 - 12 cos (x)

tanh (z) + 2 = 0

cos^{2} (a) = \frac{2}{3 sin ( a )}

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