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

The general solution for 2cos^2(θ)-cos(θ)=1 is θ=2pin,θ=(2pi)/3+2pin,θ=(4pi)/3+2pin

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2cos^2(θ)-cos(θ)=1

2 cos^{2} (θ) - cos (θ) = 1

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

Solution steps

2 cos^{2} (θ) - cos (θ) = 1

Solve by substitution

cos (θ) = 1, cos (θ) = - \frac{1}{2}

cos (θ) = 1 : θ = 2 πn

cos (θ) = - \frac{1}{2} : θ = \frac{2 π}{3} + 2 πn, θ = \frac{4 π}{3} + 2 πn

Combine all the solutions

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

sec^{2} (θ) - 4 = 0, 0 \leq θ \leq 2 π

- sin (\frac{π}{2})

tan (\frac{5 π}{12})

cos (2 0^{\circ})

arcsec (1)

What is the general solution for 2cos^2(θ)-cos(θ)=1 ?
The general solution for 2cos^2(θ)-cos(θ)=1 is θ=2pin,θ=(2pi)/3+2pin,θ=(4pi)/3+2pin