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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

-1=tan^2(θ)

- 1 = tan^{2} (θ)

No Solution for θ \in R

Solution steps

- 1 = tan^{2} (θ)

Switch sides

tan^{2} (θ) = - 1

Solve by substitution

tan^{2} (θ) = - 1

Let:

tan (θ) = u

u^{2} = - 1

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

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 (θ)

tan (θ) = i, tan (θ) = - i

tan (θ) = i, tan (θ) = - i

tan (θ) = i :

No Solution

tan (θ) = i

No Solution

tan (θ) = - i :

No Solution

tan (θ) = - i

No Solution

Combine all the solutions

No Solution for θ \in R

y, x = - cos (y)

tan (x) = \frac{3}{6}

θ, r = 1 + cos (2 θ)

tan (x) + tan (x + 4 5^{\circ}) = - 2

tan (x) = \frac{22.5}{34}

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