What is the general solution for cos^2(x)=-0.267 ?

The general solution for cos^2(x)=-0.267 is No Solution for x\in\mathbb{R}

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cos^2(x)=-0.267

cos^{2} (x) = - 0.267

No Solution for x \in R

Solution steps

cos^{2} (x) = - 0.267

Solve by substitution

cos^{2} (x) = - 0.267

Let:

cos (x) = u

u^{2} = - 0.267

u^{2} = - 0.267 : u = 0.267 i, u = - 0.267 i

u^{2} = - 0.267

For

x^{2} = f (a)

the solutions are

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

u = - 0.267, u = - - 0.267

Simplify

- 0.267 : 0.267 i

- 0.267

Apply radical rule:

- a = - 1 a

- 0.267 = - 1 0.267

= - 1 0.267

Apply imaginary number rule:

- 1 = i

= 0.267 i

Simplify

- - 0.267 : - 0.267 i

- - 0.267

Simplify

- 0.267 : 0.267 i

- 0.267

Apply radical rule:

- a = - 1 a

- 0.267 = - 1 0.267

= - 1 0.267

Apply imaginary number rule:

- 1 = i

= 0.267 i

= - 0.267 i

u = 0.267 i, u = - 0.267 i

Substitute back

u = cos (x)

cos (x) = 0.267 i, cos (x) = - 0.267 i

cos (x) = 0.267 i, cos (x) = - 0.267 i

cos (x) = 0.267 i :

No Solution

cos (x) = 0.267 i

No Solution

cos (x) = - 0.267 i :

No Solution

cos (x) = - 0.267 i

No Solution

Combine all the solutions

No Solution for x \in R

What is the general solution for cos^2(x)=-0.267 ?
The general solution for cos^2(x)=-0.267 is No Solution for x\in\mathbb{R}