What is the general solution for -tan^2(x)-1=0 ?

The general solution for -tan^2(x)-1=0 is No Solution for x\in\mathbb{R}

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-tan^2(x)-1=0

- tan^{2} (x) - 1 = 0

No Solution for x \in R

Solution steps

- tan^{2} (x) - 1 = 0

Solve by substitution

- tan^{2} (x) - 1 = 0

Let:

tan (x) = u

- u^{2} - 1 = 0

- u^{2} - 1 = 0 : u = i, u = - i

- u^{2} - 1 = 0

Move

1

to the right side

- u^{2} - 1 = 0

Add

1

to both sides

- u^{2} - 1 + 1 = 0 + 1

Simplify

- u^{2} = 1

- u^{2} = 1

Divide both sides by

- 1

- u^{2} = 1

Divide both sides by

- 1

\frac{- u ^{2}}{- 1} = \frac{1}{- 1}

Simplify

u^{2} = - 1

u^{2} = - 1

For

x^{2} = f (a)

the solutions are

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

u = - 1, u = - - 1

Simplify

- 1 : i

- 1

Apply imaginary number rule:

- 1 = i

= i

Simplify

- - 1 : - i

- - 1

Apply imaginary number rule:

- 1 = i

= - i

u = i, u = - i

Substitute back

u = tan (x)

tan (x) = i, tan (x) = - i

tan (x) = i, tan (x) = - i

tan (x) = i :

No Solution

tan (x) = i

No Solution

tan (x) = - i :

No Solution

tan (x) = - i

No Solution

Combine all the solutions

No Solution for x \in R

2 cot^{2} (y) + 3 csc (y) = 0

cot (x) = - 0.456

4 tan^{2} (θ) - 2 tan (θ) + 3 = - 7 tan (θ) + 2

- 2 = csc (θ)

2 cot (x) = csc^{2} (x)

What is the general solution for -tan^2(x)-1=0 ?
The general solution for -tan^2(x)-1=0 is No Solution for x\in\mathbb{R}