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

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

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

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

x = π + 2 πn

Solution steps

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

Solve by substitution

cos (x) = - 1, cos (x) = 2

cos (x) = - 1 : x = π + 2 πn

cos (x) = 2 :

No Solution

Combine all the solutions

x = π + 2 πn

2 - cos^{2} (x) = 4 sin^{2} (\frac{1}{2} x)

\frac{( tan ( x ) + 2 sin ( x ) )}{( tan ( x ) - 2 sin ( x ) )} = 3

sin^{(2)} (x) + cos (x) + 1 = 0

sin^{2} (θ) = 2 sin (θ)

1 - sin (2 x) = 0

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