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

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

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sin^2(x)+cos(x)=2

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

No Solution for x \in R

Solution steps

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

Subtract

2

from both sides

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

Rewrite using trig identities

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

Solve by substitution

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

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

No Solution

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

No Solution

Combine all the solutions

No Solution for x \in R

sin (θ) = - \frac{4}{5}, \frac{7 π}{2} \leq θ < 4 π, cos (2 θ)

cos (2 x) - 2 sin^{2} (x) - sin (x) = 1

- 8 sin (θ) = - 3

sin (x) + 1 = 1

- 12 cot (x) - 43 = 0

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