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

The general solution for 2tan^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 >

2tan^2(x)+1=0

Solution

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

Solution

No Solution for x \in R

Solution steps

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

Solve by substitution

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

Let:

tan (x) = u

2 u^{2} + 1 = 0

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

2 u^{2} + 1 = 0

Move

1

to the right side

2 u^{2} + 1 = 0

Subtract

1

from both sides

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

Simplify

2 u^{2} = - 1

2 u^{2} = - 1

Divide both sides by

2

2 u^{2} = - 1

Divide both sides by

2

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

Simplify

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

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

For

x^{2} = f (a)

the solutions are

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

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

Simplify

- \frac{1}{2} : i \frac{1}{2}

- \frac{1}{2}

Apply radical rule:

- a = - 1 a

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

= - 1 \frac{1}{2}

Apply imaginary number rule:

- 1 = i

= i \frac{1}{2}

Simplify

- - \frac{1}{2} : - i \frac{1}{2}

- - \frac{1}{2}

Simplify

- \frac{1}{2} : i \frac{1}{2}

- \frac{1}{2}

Apply radical rule:

- a = - 1 a

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

= - 1 \frac{1}{2}

Apply imaginary number rule:

- 1 = i

= i \frac{1}{2}

= - i \frac{1}{2}

u = i \frac{1}{2}, u = - i \frac{1}{2}

Substitute back

u = tan (x)

tan (x) = i \frac{1}{2}, tan (x) = - i \frac{1}{2}

tan (x) = i \frac{1}{2}, tan (x) = - i \frac{1}{2}

tan (x) = i \frac{1}{2} :

No Solution

tan (x) = i \frac{1}{2}

No Solution

tan (x) = - i \frac{1}{2} :

No Solution

tan (x) = - i \frac{1}{2}

No Solution

Combine all the solutions

No Solution for x \in R

Popular Examples

solvefor y,arctan(y)=(x^3)/3-2x+c solve for

y, arctan (y) = \frac{x ^{3}}{3} - 2 x + c

cos(A)= 3/4

cos (A) = \frac{3}{4}

3cos(x)=sqrt(2)cot(x)

3 cos (x) = 2 cot (x)

5cos(7θ)=0

5 cos (7 θ) = 0

-8tan(y)=0

- 8 tan (y) = 0

Frequently Asked Questions (FAQ)

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