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

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

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

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

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

Solution steps

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

Solve by substitution

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

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

cos (x) = - 1 : x = π + 2 πn

Combine all the solutions

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

cos (θ) = cos (1)

tan (\frac{x}{2}) = \pm \frac{1 - cos ( x )}{1 + cos ( x )}

sin^{2} (x) - cos^{2} (x) = 0.5

sec (x) - tan (x) = 1

7 cos^{2} (θ) + 6 cos (θ) - 12 = 7 cos (θ) - 6

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