What is the general solution for 2cos^2(θ)-11cos(θ)+5=0 ?

The general solution for 2cos^2(θ)-11cos(θ)+5=0 is θ= pi/3+2pin,θ=(5pi)/3+2pin

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2cos^2(θ)-11cos(θ)+5=0

2 cos^{2} (θ) - 11 cos (θ) + 5 = 0

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

Solution steps

2 cos^{2} (θ) - 11 cos (θ) + 5 = 0

Solve by substitution

cos (θ) = 5, cos (θ) = \frac{1}{2}

cos (θ) = 5 :

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

4 sin (2 x) - 1 = 0

cos (2 x) - 3 sin (2 x) = 0

x, cos (x) + sin (x) = 0

sin (x) (2 cos (x) - 1) = 0

cos (θ) = 1 + 2 sec (θ)

What is the general solution for 2cos^2(θ)-11cos(θ)+5=0 ?
The general solution for 2cos^2(θ)-11cos(θ)+5=0 is θ= pi/3+2pin,θ=(5pi)/3+2pin