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

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

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sin^2(x)=3

sin^{2} (x) = 3

No Solution for x \in R

Solution steps

sin^{2} (x) = 3

Solve by substitution

sin^{2} (x) = 3

Let:

sin (x) = u

u^{2} = 3

u^{2} = 3 : u = 3, u = - 3

u^{2} = 3

For

x^{2} = f (a)

the solutions are

x = f (a), - f (a)

u = 3, u = - 3

Substitute back

u = sin (x)

sin (x) = 3, sin (x) = - 3

sin (x) = 3, sin (x) = - 3

sin (x) = 3 :

No Solution

sin (x) = 3

- 1 \leq sin (x) \leq 1

No Solution

sin (x) = - 3 :

No Solution

sin (x) = - 3

- 1 \leq sin (x) \leq 1

No Solution

Combine all the solutions

No Solution for x \in R

2 cos (2 θ) - 2 = - 3 sin (θ)

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

sin (\frac{π}{6} + x) + sin (\frac{π}{6} - x) = \frac{1}{2}

csc (θ) = \frac{7}{3}

6 sin (θ) = 3

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