What is the general solution for cos(θ)+2cos^2(θ)=1 ?

The general solution for cos(θ)+2cos^2(θ)=1 is θ= pi/3+2pin,θ=(5pi)/3+2pin,θ=pi+2pin

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cos(θ)+2cos^2(θ)=1

cos (θ) + 2 cos^{2} (θ) = 1

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

Solution steps

cos (θ) + 2 cos^{2} (θ) = 1

Solve by substitution

cos (θ) = \frac{1}{2}, cos (θ) = - 1

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

cos (θ) = - 1 : θ = π + 2 πn

Combine all the solutions

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

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

sin^{2} (θ) - cos^{2} (θ) = 1 + cos (θ), 0 \leq θ < 2 π

csc (x) = \frac{1}{2}

sin^{2} (θ) - sin (θ) = 0

2 cos^{2} (x) - 1 = 0, 0 \leq x < 2 π

What is the general solution for cos(θ)+2cos^2(θ)=1 ?
The general solution for cos(θ)+2cos^2(θ)=1 is θ= pi/3+2pin,θ=(5pi)/3+2pin,θ=pi+2pin