What is the general solution for cos^2(x)-2cos(x)=3 ?

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

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cos^2(x)-2cos(x)=3

cos^{2} (x) - 2 cos (x) = 3

x = π + 2 πn

Solution steps

cos^{2} (x) - 2 cos (x) = 3

Solve by substitution

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

cos (x) = 3 :

No Solution

cos (x) = - 1 : x = π + 2 πn

Combine all the solutions

x = π + 2 πn

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

2 sin^{2} (x) = 1, + [0, + 2 π]

3 sin (x) - 2 sin (x) cos (x) = 0

sin (x) = \frac{33}{80}

3 sin (x) + 5 = - 2 sin (x)

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