What is the general solution for cos^2(x)=-1 ?

The general solution for cos^2(x)=-1 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 >

cos^2(x)=-1

cos^{2} (x) = - 1

No Solution for x \in R

Solution steps

cos^{2} (x) = - 1

Solve by substitution

cos^{2} (x) = - 1

Let:

cos (x) = 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 = cos (x)

cos (x) = i, cos (x) = - i

cos (x) = i, cos (x) = - i

cos (x) = i :

No Solution

cos (x) = i

No Solution

cos (x) = - i :

No Solution

cos (x) = - i

No Solution

Combine all the solutions

No Solution for x \in R

cos (2 x) = 1 - sin (x)

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

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

cos (2 x) + 3 sin (x) + 1 = 0

cos (z) = 2

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