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

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

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sin^2(θ)-cos^2(θ)=cos(θ)

sin^{2} (θ) - cos^{2} (θ) = cos (θ)

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

Solution steps

sin^{2} (θ) - cos^{2} (θ) = cos (θ)

Subtract

cos (θ)

from both sides

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) = - 1, cos (θ) = \frac{1}{2}

cos (θ) = - 1 : θ = π + 2 πn

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

Combine all the solutions

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

csc (t) = 2

arccosh (θ) = 0.86806

sin (t) = \frac{5}{13}

sin (x) = - \frac{7}{4}

cos^{2} (x) = 4 (1 + sin (x))

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