What is the general solution for tan^2(x/2)=-2 ?

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

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tan^2(x/2)=-2

tan^{2} (\frac{x}{2}) = - 2

No Solution for x \in R

Solution steps

tan^{2} (\frac{x}{2}) = - 2

Solve by substitution

tan^{2} (\frac{x}{2}) = - 2

Let:

tan (\frac{x}{2}) = u

u^{2} = - 2

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

u^{2} = - 2

For

x^{2} = f (a)

the solutions are

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

u = - 2, u = - - 2

Simplify

- 2 : 2 i

- 2

Apply radical rule:

- a = - 1 a

- 2 = - 1 2

= - 1 2

Apply imaginary number rule:

- 1 = i

= 2 i

Simplify

- - 2 : - 2 i

- - 2

Simplify

- 2 : 2 i

- 2

Apply radical rule:

- a = - 1 a

- 2 = - 1 2

= - 1 2

Apply imaginary number rule:

- 1 = i

= 2 i

= - 2 i

u = 2 i, u = - 2 i

Substitute back

u = tan (\frac{x}{2})

tan (\frac{x}{2}) = 2 i, tan (\frac{x}{2}) = - 2 i

tan (\frac{x}{2}) = 2 i, tan (\frac{x}{2}) = - 2 i

tan (\frac{x}{2}) = 2 i :

No Solution

tan (\frac{x}{2}) = 2 i

No Solution

tan (\frac{x}{2}) = - 2 i :

No Solution

tan (\frac{x}{2}) = - 2 i

No Solution

Combine all the solutions

No Solution for x \in R

sin^{2} (θ) - 1 = 2 sin (θ)

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

16 sin (3 x) cos (x) + 83 sin (3 x) - 2 cos (x) - 3 = 0

tan (C) = 2.56

cos (3 y) = 0

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