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

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

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cos^2(θ)=2+2sin(θ)

cos^{2} (θ) = 2 + 2 sin (θ)

θ = \frac{3 π}{2} + 2 πn

Solution steps

cos^{2} (θ) = 2 + 2 sin (θ)

Subtract

2 + 2 sin (θ)

from both sides

cos^{2} (θ) - 2 - 2 sin (θ) = 0

Rewrite using trig identities

- 1 - sin^{2} (θ) - 2 sin (θ) = 0

Solve by substitution

sin (θ) = - 1

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

Combine all the solutions

θ = \frac{3 π}{2} + 2 πn

cos (x) - 2 cos (x) sin (x) = 0

2 sec^{2} (x) = 0

2 cos (3 θ) = - 1

1 + sin (2 x) = 0

2 cos^{2} (x) + 3 cos (x) - 3 = 0

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