What is the general solution for cos^2(x)+4cos(x)+3=0 ?

The general solution for cos^2(x)+4cos(x)+3=0 is x=pi+2pin

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cos^2(x)+4cos(x)+3=0

cos^{2} (x) + 4 cos (x) + 3 = 0

x = π + 2 πn

Solution steps

cos^{2} (x) + 4 cos (x) + 3 = 0

Solve by substitution

cos (x) = - 1, cos (x) = - 3

cos (x) = - 1 : x = π + 2 πn

cos (x) = - 3 :

No Solution

Combine all the solutions

x = π + 2 πn

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

2 sin^{2} (x) - sin (x) - 1 = 0, 0 \leq x < 2 π

sin^{2} (x) = 3

2 cos (2 θ) - 2 = - 3 sin (θ)

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

What is the general solution for cos^2(x)+4cos(x)+3=0 ?
The general solution for cos^2(x)+4cos(x)+3=0 is x=pi+2pin