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

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

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cos^2(z)=-1

cos^{2} (z) = - 1

No Solution for z \in R

Solution steps

cos^{2} (z) = - 1

Solve by substitution

cos^{2} (z) = - 1

Let:

cos (z) = 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 (z)

cos (z) = i, cos (z) = - i

cos (z) = i, cos (z) = - i

cos (z) = i :

No Solution

cos (z) = i

No Solution

cos (z) = - i :

No Solution

cos (z) = - i

No Solution

Combine all the solutions

No Solution for z \in R

cosh (x) = \frac{6}{2}

tan (x) - sec (x) = 3, 0 \leq x < 2 π

sin^{2} (θ) + 2 cos^{2} (θ) = 4

2 sin (3 x) = - 3

8 - 12 sin^{2} (x) = 4 cos^{2} (x)

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