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

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

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2cos^2(θ)-5cos(θ)=3

2 cos^{2} (θ) - 5 cos (θ) = 3

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

Solution steps

2 cos^{2} (θ) - 5 cos (θ) = 3

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

12 sin^{2} (x) - 20 sin (x) = - 8

6 arccos (4 x) = π

- 4 sin (x) cos (x) = 2 sin (x)

7 sin^{2} (θ) + 16 sin (θ) + 9 = 0

3 tan (\frac{3 π}{4} (x + \frac{3 π}{2})) = 1

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