What is the general solution for 2cos^2(θ)=7cos(θ)-3 ?

The general solution for 2cos^2(θ)=7cos(θ)-3 is θ= pi/3+2pin,θ=(5pi)/3+2pin

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2cos^2(θ)=7cos(θ)-3

2 cos^{2} (θ) = 7 cos (θ) - 3

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

Solution steps

2 cos^{2} (θ) = 7 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{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

sin (θ) = (\frac{173}{210})

\frac{3 tan ^{2} ( x ) - 5}{cos ( x ) + 1} = 0

sin (3 x) = \frac{1}{2}, 0 \leq x \leq 2 π

cos (θ) = sec (θ), 0 \leq θ < 2 π

\frac{441}{841} + sin^{2} (t) = 1

What is the general solution for 2cos^2(θ)=7cos(θ)-3 ?
The general solution for 2cos^2(θ)=7cos(θ)-3 is θ= pi/3+2pin,θ=(5pi)/3+2pin