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

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

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cos^2(θ)-cos(θ)=sin^2(θ)

cos^{2} (θ) - cos (θ) = sin^{2} (θ)

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

Solution steps

cos^{2} (θ) - cos (θ) = sin^{2} (θ)

Subtract

sin^{2} (θ)

from both sides

cos^{2} (θ) - cos (θ) - sin^{2} (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 = 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

sin (x) + 2 sin^{2} (x) = 0

5 sec^{2} (x) - 5 = 0, 0 \leq x \leq 2 π

4 cos^{2} (θ) + 4 = 5

4 sin (2 z) - 3 cos (z) = 0

0.34 = cos (x)

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