What is the general solution for cos^2(θ)-3/2 = 5/2 cos(θ) ?

The general solution for cos^2(θ)-3/2 = 5/2 cos(θ) is θ=(2pi)/3+2pin,θ=(4pi)/3+2pin

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cos^2(θ)-3/2 = 5/2 cos(θ)

cos^{2} (θ) - \frac{3}{2} = \frac{5}{2} cos (θ)

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

Solution steps

cos^{2} (θ) - \frac{3}{2} = \frac{5}{2} cos (θ)

Solve by substitution

cos (θ) = 3, cos (θ) = - \frac{1}{2}

cos (θ) = 3 :

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

tan (x) = - \frac{1}{8}

sin (x) cot (x) = 1

sin (θ) = 0.4484

sin (5 x - 28) = cos (3 x - 50)

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

What is the general solution for cos^2(θ)-3/2 = 5/2 cos(θ) ?
The general solution for cos^2(θ)-3/2 = 5/2 cos(θ) is θ=(2pi)/3+2pin,θ=(4pi)/3+2pin