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

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

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

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

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

Solution steps

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

2 sin (2 x) + 1 = 0

sin (θ) = \frac{5}{13}

sin^{2} (x) = 2 sin (x) + 3

2 cos^{2} (θ) - sin (θ) = 1

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