What is the general solution for cos^2(θ)=3(1-sin(θ)) ?

The general solution for cos^2(θ)=3(1-sin(θ)) is θ= pi/2+2pin

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cos^2(θ)=3(1-sin(θ))

cos^{2} (θ) = 3 (1 - sin (θ))

θ = \frac{π}{2} + 2 πn

Solution steps

cos^{2} (θ) = 3 (1 - sin (θ))

Subtract

3 (1 - sin (θ))

from both sides

cos^{2} (θ) - 3 (1 - sin (θ)) = 0

Rewrite using trig identities

- 2 - sin^{2} (θ) + 3 sin (θ) = 0

Solve by substitution

sin (θ) = 1, sin (θ) = 2

sin (θ) = 1 : θ = \frac{π}{2} + 2 πn

sin (θ) = 2 :

No Solution

Combine all the solutions

θ = \frac{π}{2} + 2 πn

cos (x) = \frac{13}{20}

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

2 sin^{2} (x) + sin (x) = 1, 0 \leq x < 2 π

cos (\frac{7 π}{8} - x) = \frac{2}{2}

5 sin^{2} (x) + 3 sin (x) = 2

What is the general solution for cos^2(θ)=3(1-sin(θ)) ?
The general solution for cos^2(θ)=3(1-sin(θ)) is θ= pi/2+2pin