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

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

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sin^2(x)= 3/2

sin^{2} (x) = \frac{3}{2}

No Solution for x \in R

Solution steps

sin^{2} (x) = \frac{3}{2}

Solve by substitution

sin^{2} (x) = \frac{3}{2}

Let:

sin (x) = u

u^{2} = \frac{3}{2}

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

u^{2} = \frac{3}{2}

For

x^{2} = f (a)

the solutions are

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

u = \frac{3}{2}, u = - \frac{3}{2}

Substitute back

u = sin (x)

sin (x) = \frac{3}{2}, sin (x) = - \frac{3}{2}

sin (x) = \frac{3}{2}, sin (x) = - \frac{3}{2}

sin (x) = \frac{3}{2} :

No Solution

sin (x) = \frac{3}{2}

- 1 \leq sin (x) \leq 1

No Solution

sin (x) = - \frac{3}{2} :

No Solution

sin (x) = - \frac{3}{2}

- 1 \leq sin (x) \leq 1

No Solution

Combine all the solutions

No Solution for x \in R

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tan (3 b + 14) = cot (5 b + 4)

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

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