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

The general solution for cos^2(θ)+sin(θ)=2 is No Solution for θ\in\mathbb{R}

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cos^2(θ)+sin(θ)=2

cos^{2} (θ) + sin (θ) = 2

No Solution for θ \in R

Solution steps

cos^{2} (θ) + sin (θ) = 2

Subtract

2

from both sides

cos^{2} (θ) + sin (θ) - 2 = 0

Rewrite using trig identities

- 1 + sin (θ) - sin^{2} (θ) = 0

Solve by substitution

sin (θ) = \frac{1}{2} - i \frac{3}{2}, sin (θ) = \frac{1}{2} + i \frac{3}{2}

sin (θ) = \frac{1}{2} - i \frac{3}{2} :

No Solution

sin (θ) = \frac{1}{2} + i \frac{3}{2} :

No Solution

Combine all the solutions

No Solution for θ \in R

3 tan^{2} (θ) + tan (θ) = 0

6 sin (θ) + 1 = 4 sin (θ)

tan (t) = - \frac{1}{3}

0 = 2 cos (θ) sin (θ) + cos (θ)

sin (x) = \frac{1}{2} tan (x)

What is the general solution for cos^2(θ)+sin(θ)=2 ?
The general solution for cos^2(θ)+sin(θ)=2 is No Solution for θ\in\mathbb{R}