What is the general solution for cos^2(a)=2 ?

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

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cos^2(a)=2

cos^{2} (a) = 2

No Solution for a \in R

Solution steps

cos^{2} (a) = 2

Solve by substitution

cos^{2} (a) = 2

Let:

cos (a) = u

u^{2} = 2

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

u^{2} = 2

For

x^{2} = f (a)

the solutions are

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

u = 2, u = - 2

Substitute back

u = cos (a)

cos (a) = 2, cos (a) = - 2

cos (a) = 2, cos (a) = - 2

cos (a) = 2 :

No Solution

cos (a) = 2

- 1 \leq cos (x) \leq 1

No Solution

cos (a) = - 2 :

No Solution

cos (a) = - 2

- 1 \leq cos (x) \leq 1

No Solution

Combine all the solutions

No Solution for a \in R

arctan (2 x) = - \frac{16}{10}

3 tan (x) + 4 = 0

x, sin (x) = - \frac{3}{2}

\frac{7 π}{2} = 7 - 3 sin (x)

- 10 sin (y) = 0

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