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

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

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2=cos^2(x)

2 = cos^{2} (x)

No Solution for x \in R

Solution steps

2 = cos^{2} (x)

Switch sides

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

(tan (x) - 1) (sin (x) - 1) = 0

\frac{1}{cos ( 2 x )} + tan (2 x) = 3 cos (2 x), 0^{\circ} < x < 9 0^{\circ}

sin (x) = \frac{4}{5}, 0 \leq x < 2 π

7 sin^{2} (θ) - 5 sin (θ) = 2

sec (2 x) = - (\frac{2}{3})

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