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}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Subtract

1

from both sides

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

sec (θ) = \frac{- 2 3}{3}

2 sin^{2} (x) - 3 sin (x) + 1 = 0, 0 \leq x \leq 2 π

16 sin^{2} (x) - 1 = 0

4 cos^{2} (x) + 4 cos (x) = - 1

tan (x) = 6

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}