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

The general solution for -2=tan^2(x) 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 >

-2=tan^2(x)

- 2 = tan^{2} (x)

No Solution for x \in R

Solution steps

- 2 = tan^{2} (x)

Switch sides

tan^{2} (x) = - 2

Solve by substitution

tan^{2} (x) = - 2

Let:

tan (x) = 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 (x)

tan (x) = 2 i, tan (x) = - 2 i

tan (x) = 2 i, tan (x) = - 2 i

tan (x) = 2 i :

No Solution

tan (x) = 2 i

No Solution

tan (x) = - 2 i :

No Solution

tan (x) = - 2 i

No Solution

Combine all the solutions

No Solution for x \in R

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

sin (3 \cdot x) = cos (x)

sin^{22} (x) = sin^{2} (x)

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

cos (8 t) - 5 sin (8 t) = 0

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