What is the general solution for cos(2θ)-3cos(θ)+2=0 ?

The general solution for cos(2θ)-3cos(θ)+2=0 is θ=2pin,θ= pi/3+2pin,θ=(5pi)/3+2pin

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cos(2θ)-3cos(θ)+2=0

cos (2 θ) - 3 cos (θ) + 2 = 0

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

Solution steps

cos (2 θ) - 3 cos (θ) + 2 = 0

Rewrite using trig identities

1 + 2 cos^{2} (θ) - 3 cos (θ) = 0

Solve by substitution

cos (θ) = 1, cos (θ) = \frac{1}{2}

cos (θ) = 1 : θ = 2 πn

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

Combine all the solutions

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

u, x = 2 tanh (u)

4 cos^{2} (x) + cos (2 x) - 7 cos (x) = - 2

4 cos (x) = 2 + 2 cos (x)

4 cos (θ) = 43 sin (θ)

- 4 sin (θ) = 4 (sin (θ) - 1)

What is the general solution for cos(2θ)-3cos(θ)+2=0 ?
The general solution for cos(2θ)-3cos(θ)+2=0 is θ=2pin,θ= pi/3+2pin,θ=(5pi)/3+2pin