What is the general solution for sin^2(x)=14 ?

The general solution for sin^2(x)=14 is No Solution for x\in\mathbb{R}

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sin^2(x)=14

sin^{2} (x) = 14

No Solution for x \in R

Solution steps

sin^{2} (x) = 14

Solve by substitution

sin^{2} (x) = 14

Let:

sin (x) = u

u^{2} = 14

u^{2} = 14 : u = 14, u = - 14

u^{2} = 14

For

x^{2} = f (a)

the solutions are

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

u = 14, u = - 14

Substitute back

u = sin (x)

sin (x) = 14, sin (x) = - 14

sin (x) = 14, sin (x) = - 14

sin (x) = 14 :

No Solution

sin (x) = 14

- 1 \leq sin (x) \leq 1

No Solution

sin (x) = - 14 :

No Solution

sin (x) = - 14

- 1 \leq sin (x) \leq 1

No Solution

Combine all the solutions

No Solution for x \in R

sin (2 x) \cdot cos (3 x) = 0

sin^{2} (x) = - 3

cos (θ) = - \frac{2}{7}

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

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

What is the general solution for sin^2(x)=14 ?
The general solution for sin^2(x)=14 is No Solution for x\in\mathbb{R}