What is the general solution for cos^2(x)=-1.5 ?

The general solution for cos^2(x)=-1.5 is No Solution for x\in\mathbb{R}

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cos^2(x)=-1.5

cos^{2} (x) = - 1.5

No Solution for x \in R

Solution steps

cos^{2} (x) = - 1.5

Solve by substitution

cos^{2} (x) = - 1.5

Let:

cos (x) = u

u^{2} = - 1.5

u^{2} = - 1.5 : u = 1.5 i, u = - 1.5 i

u^{2} = - 1.5

For

x^{2} = f (a)

the solutions are

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

u = - 1.5, u = - - 1.5

Simplify

- 1.5 : 1.5 i

- 1.5

Apply radical rule:

- a = - 1 a

- 1.5 = - 1 1.5

= - 1 1.5

Apply imaginary number rule:

- 1 = i

= 1.5 i

Simplify

- - 1.5 : - 1.5 i

- - 1.5

Simplify

- 1.5 : 1.5 i

- 1.5

Apply radical rule:

- a = - 1 a

- 1.5 = - 1 1.5

= - 1 1.5

Apply imaginary number rule:

- 1 = i

= 1.5 i

= - 1.5 i

u = 1.5 i, u = - 1.5 i

Substitute back

u = cos (x)

cos (x) = 1.5 i, cos (x) = - 1.5 i

cos (x) = 1.5 i, cos (x) = - 1.5 i

cos (x) = 1.5 i :

No Solution

cos (x) = 1.5 i

No Solution

cos (x) = - 1.5 i :

No Solution

cos (x) = - 1.5 i

No Solution

Combine all the solutions

No Solution for x \in R

2 arctan (\frac{1}{2}) - arctan (x) = \frac{π}{4}

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

sin (θ) = \frac{13}{85}

sin (2 x) = \frac{( 6 m - 5 )}{8}

cos (θ) = \frac{3}{45}

What is the general solution for cos^2(x)=-1.5 ?
The general solution for cos^2(x)=-1.5 is No Solution for x\in\mathbb{R}