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

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

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

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

No Solution for x \in R

Solution steps

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

Subtract

2 - cos (x)

from both sides

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

cos (2 x) = \frac{2}{2}, 0 \leq x \leq 2 π

sin (2 x) cos (x) = 0

8 cos (x) + 8 sin (x) tan (x) = 16

(sin (2 x) - 1) (2 sin (2 x) - 1) = 0

2 cos^{2} (x) - cos (x) = 2 - sec (x)

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