What is the general solution for cos^2(x)=4 ?

The general solution for cos^2(x)=4 is No Solution for x\in\mathbb{R}

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cos^2(x)=4

cos^{2} (x) = 4

No Solution for x \in R

Solution steps

cos^{2} (x) = 4

Solve by substitution

cos^{2} (x) = 4

Let:

cos (x) = u

u^{2} = 4

u^{2} = 4 : u = 2, u = - 2

u^{2} = 4

For

x^{2} = f (a)

the solutions are

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

u = 4, u = - 4

4 = 2

4

Factor the number:

4 = 2^{2}

= 2^{2}

Apply radical rule:

2^{2} = 2

= 2

- 4 = - 2

- 4

4 = 2

4

Factor the number:

4 = 2^{2}

= 2^{2}

Apply radical rule:

2^{2} = 2

= 2

= - 2

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 tan (θ) - sec (θ) = 0

4 cos (x) = - sin^{2} (x) + 1, 0 \leq x \leq 2 π

2 \cdot sin (x) = tan (x)

0 = arcsin (x)

cos (x) = 0.5149, 0 \leq x < 2 π

What is the general solution for cos^2(x)=4 ?
The general solution for cos^2(x)=4 is No Solution for x\in\mathbb{R}