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

The general solution for sin^2(θ)=2cos(θ)+2 is θ=pi+2pin

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sin^2(θ)=2cos(θ)+2

sin^{2} (θ) = 2 cos (θ) + 2

θ = π + 2 πn

Solution steps

sin^{2} (θ) = 2 cos (θ) + 2

Subtract

2 cos (θ) + 2

from both sides

sin^{2} (θ) - 2 cos (θ) - 2 = 0

Rewrite using trig identities

- 1 - cos^{2} (θ) - 2 cos (θ) = 0

Solve by substitution

cos (θ) = - 1

cos (θ) = - 1 : θ = π + 2 πn

Combine all the solutions

θ = π + 2 πn

cos (4 x) (cos (x) - 1) = 0

3 tan (\frac{x}{2}) + 3 = 0

4 cos (x) tan (x) = 5 tan (x)

4 cos^{2} (2 x) - 1 = 0

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

What is the general solution for sin^2(θ)=2cos(θ)+2 ?
The general solution for sin^2(θ)=2cos(θ)+2 is θ=pi+2pin