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 i, u = - 3 i

u^{2} = - 3

For

x^{2} = f (a)

the solutions are

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

u = - 3, u = - - 3

Simplify

- 3 : 3 i

- 3

Apply radical rule:

- a = - 1 a

- 3 = - 1 3

= - 1 3

Apply imaginary number rule:

- 1 = i

= 3 i

Simplify

- - 3 : - 3 i

- - 3

Simplify

- 3 : 3 i

- 3

Apply radical rule:

- a = - 1 a

- 3 = - 1 3

= - 1 3

Apply imaginary number rule:

- 1 = i

= 3 i

= - 3 i

u = 3 i, u = - 3 i

Substitute back

u = sin (x)

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

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

sin (x) = 3 i :

No Solution

sin (x) = 3 i

No Solution

sin (x) = - 3 i :

No Solution

sin (x) = - 3 i

No Solution

Combine all the solutions

No Solution for x \in R

cos (θ) = - \frac{2}{7}

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

cos (x) = - \frac{7}{14 5}

k, cos (k l) = 0

tan (2 x) = - \frac{- 270 - 120}{130}

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}