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

The general solution for cos(2x)-3cos(x)=-2 is x=2pin,x= pi/3+2pin,x=(5pi)/3+2pin

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

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

x = 2 πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Solution steps

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

Subtract

- 2

from both sides

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

Rewrite using trig identities

1 + 2 cos^{2} (x) - 3 cos (x) = 0

Solve by substitution

cos (x) = 1, cos (x) = \frac{1}{2}

cos (x) = 1 : x = 2 πn

cos (x) = \frac{1}{2} : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Combine all the solutions

x = 2 πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

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

cos^{2} (3 x) = cos (9 x^{2})

2 cos (θ) - 2 = 0

x, y = r (sec (x))

csc^{2} (x) - 3 = 6 tan (x)

What is the general solution for cos(2x)-3cos(x)=-2 ?
The general solution for cos(2x)-3cos(x)=-2 is x=2pin,x= pi/3+2pin,x=(5pi)/3+2pin