What is the general solution for 2cos^2(θ)-4=3cos(θ)-2 ?

The general solution for 2cos^2(θ)-4=3cos(θ)-2 is θ=(2pi)/3+2pin,θ=(4pi)/3+2pin

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2cos^2(θ)-4=3cos(θ)-2

2 cos^{2} (θ) - 4 = 3 cos (θ) - 2

θ = \frac{2 π}{3} + 2 πn, θ = \frac{4 π}{3} + 2 πn

Solution steps

2 cos^{2} (θ) - 4 = 3 cos (θ) - 2

Solve by substitution

cos (θ) = 2, cos (θ) = - \frac{1}{2}

cos (θ) = 2 :

No Solution

cos (θ) = - \frac{1}{2} : θ = \frac{2 π}{3} + 2 πn, θ = \frac{4 π}{3} + 2 πn

Combine all the solutions

θ = \frac{2 π}{3} + 2 πn, θ = \frac{4 π}{3} + 2 πn

cos (x) = 1.2

cot (x) = 2 cos (x)

(cot (x) - 1) (3 cot (x) - 1) = 0

sin (2 θ) + 2 cos (θ) = 0

cot (3 x) = 0, 0 \leq x \leq 2 π

What is the general solution for 2cos^2(θ)-4=3cos(θ)-2 ?
The general solution for 2cos^2(θ)-4=3cos(θ)-2 is θ=(2pi)/3+2pin,θ=(4pi)/3+2pin