find all solution to cos^2x+cosx=0

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embizze | High School Teacher | (Level 1) Educator Emeritus

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The answer above is incomplete. The domain of `cos^(-1)x` is `[0,pi)` . `cos^(-1)0=pi/2` but `cosx=0` if `x=(3pi)/2` also.

The complete solution is `x=pi/2 +npi,x=pi+2npi` for `n in ZZ`

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The solution to the equation `cos^2x + cos x = 0` has to be determined.

`cos^2x + cos x = 0`

=> `cos x(cos x + 1) = 0`

=> cos x = 0 and cos x = -1

=> x = `cos^-1 0` and x =`cos^-1(-1)`

=> x = `pi/2 + 2*n*pi` and x = `pi + 2*n*pi`

The solution of the equation cos^2x + cos x = 0 is `x = pi/2 + 2*n*pi` and `x = pi + 2*n*pi`

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