What is the general solution for 2cos^2(θ)-9cos(θ)+4=0 ?

The general solution for 2cos^2(θ)-9cos(θ)+4=0 is θ= pi/3+2pin,θ=(5pi)/3+2pin

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2cos^2(θ)-9cos(θ)+4=0

2 cos^{2} (θ) - 9 cos (θ) + 4 = 0

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

Solution steps

2 cos^{2} (θ) - 9 cos (θ) + 4 = 0

Solve by substitution

cos (θ) = 4, cos (θ) = \frac{1}{2}

cos (θ) = 4 :

No Solution

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

Combine all the solutions

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

cos (2 x + \frac{π}{4}) = \frac{2}{2}

x, tan (x) = 1

cot (t) = - 3

tan (x) = \frac{3}{8}

1 - sin (x) = 2 cos^{2} (x)

What is the general solution for 2cos^2(θ)-9cos(θ)+4=0 ?
The general solution for 2cos^2(θ)-9cos(θ)+4=0 is θ= pi/3+2pin,θ=(5pi)/3+2pin