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

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

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sin^2(θ)+cos(θ)=2

sin^{2} (θ) + cos (θ) = 2

No Solution for θ \in R

Solution steps

sin^{2} (θ) + cos (θ) = 2

Subtract

2

from both sides

sin^{2} (θ) + cos (θ) - 2 = 0

Rewrite using trig identities

- 1 + cos (θ) - cos^{2} (θ) = 0

Solve by substitution

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

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

No Solution

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

No Solution

Combine all the solutions

No Solution for θ \in R

cot (2 x) - 1 = 0

tan (2 θ) - tan (θ) = 0, 0 < θ < 2 π

- 8 cos (x) = - 6 sec (x) + 8

cos (2 θ) + sin (θ) = 1

sin (x) - 2 cos (x) = 1

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