What is the general solution for tan^2(x)+3=0 ?

The general solution for tan^2(x)+3=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)+3=0

tan^{2} (x) + 3 = 0

No Solution for x \in R

Solution steps

tan^{2} (x) + 3 = 0

Solve by substitution

tan^{2} (x) + 3 = 0

Let:

tan (x) = u

u^{2} + 3 = 0

u^{2} + 3 = 0 : u = 3 i, u = - 3 i

u^{2} + 3 = 0

Move

3

to the right side

u^{2} + 3 = 0

Subtract

3

from both sides

u^{2} + 3 - 3 = 0 - 3

Simplify

u^{2} = - 3

u^{2} = - 3

For

x^{2} = f (a)

the solutions are

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

u = - 3, u = - - 3

Simplify

- 3 : 3 i

- 3

Apply radical rule:

- a = - 1 a

- 3 = - 1 3

= - 1 3

Apply imaginary number rule:

- 1 = i

= 3 i

Simplify

- - 3 : - 3 i

- - 3

Simplify

- 3 : 3 i

- 3

Apply radical rule:

- a = - 1 a

- 3 = - 1 3

= - 1 3

Apply imaginary number rule:

- 1 = i

= 3 i

= - 3 i

u = 3 i, u = - 3 i

Substitute back

u = tan (x)

tan (x) = 3 i, tan (x) = - 3 i

tan (x) = 3 i, tan (x) = - 3 i

tan (x) = 3 i :

No Solution

tan (x) = 3 i

No Solution

tan (x) = - 3 i :

No Solution

tan (x) = - 3 i

No Solution

Combine all the solutions

No Solution for x \in R

4 cos (θ) + 1 = 0

cos (a) = \frac{3}{- 6}

cos (x + 5) = \frac{1}{2} 3, 0 \leq x \leq 2 π

cos^{2} (x) = 3 sin^{2} (x)

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

What is the general solution for tan^2(x)+3=0 ?
The general solution for tan^2(x)+3=0 is No Solution for x\in\mathbb{R}