What is the general solution for sin^2(x)-2sin(x)+3=0 ?

The general solution for sin^2(x)-2sin(x)+3=0 is No Solution for x\in\mathbb{R}

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sin^2(x)-2sin(x)+3=0

sin^{2} (x) - 2 sin (x) + 3 = 0

No Solution for x \in R

Solution steps

sin^{2} (x) - 2 sin (x) + 3 = 0

Solve by substitution

sin (x) = 1 + 2 i, sin (x) = 1 - 2 i

sin (x) = 1 + 2 i :

No Solution

sin (x) = 1 - 2 i :

No Solution

Combine all the solutions

No Solution for x \in R

csc^{2} (x) - csc (x) = 2

cos (4 x) = \frac{- 1}{2}

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

2 cos^{2} (x) - 3 cos (x) + 1 = 0, 0 \leq x \leq 2 π

cos^{2} (a) = \frac{1}{2}

What is the general solution for sin^2(x)-2sin(x)+3=0 ?
The general solution for sin^2(x)-2sin(x)+3=0 is No Solution for x\in\mathbb{R}