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

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

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cos^2(x)=2

cos^{2} (x) = 2

No Solution for x \in R

Solution steps

cos^{2} (x) = 2

Solve by substitution

cos^{2} (x) = 2

Let:

cos (x) = 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 (x)

cos (x) = 2, cos (x) = - 2

cos (x) = 2, cos (x) = - 2

cos (x) = 2 :

No Solution

cos (x) = 2

- 1 \leq cos (x) \leq 1

No Solution

cos (x) = - 2 :

No Solution

cos (x) = - 2

- 1 \leq cos (x) \leq 1

No Solution

Combine all the solutions

No Solution for x \in R

2 sin^{2} (x) = 3 cos (x)

5 cos (θ) + 3 = 3 cos (θ) + 5

6 sec^{2} (x) - 8 = 0

(2 sin (2 x) + 3) (- 3 + tan^{2} (3 x)) = 0

tan (3 x) = 1, 0 \leq x \leq 2 π

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