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

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

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sin^2(θ)-cos^2(θ)+cos(θ)=0

sin^{2} (θ) - cos^{2} (θ) + cos (θ) = 0

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

Solution steps

sin^{2} (θ) - cos^{2} (θ) + cos (θ) = 0

Rewrite using trig identities

1 + cos (θ) - 2 cos^{2} (θ) = 0

Solve by substitution

cos (θ) = - \frac{1}{2}, cos (θ) = 1

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

cos (θ) = 1 : θ = 2 πn

Combine all the solutions

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

3 sin^{2} (x) = 9 cos^{2} (x)

sin (\frac{1}{2 x}) = - 1

3 cos^{2} (x) - 3 = sin (x)

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

cos (x) = - \frac{3}{10}

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