What is the general solution for cos^2(x)= 3/2 ?

The general solution for cos^2(x)= 3/2 is No Solution for x\in\mathbb{R}

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cos^2(x)= 3/2

cos^{2} (x) = \frac{3}{2}

No Solution for x \in R

Solution steps

cos^{2} (x) = \frac{3}{2}

Solve by substitution

cos^{2} (x) = \frac{3}{2}

Let:

cos (x) = u

u^{2} = \frac{3}{2}

u^{2} = \frac{3}{2} : u = \frac{3}{2}, u = - \frac{3}{2}

u^{2} = \frac{3}{2}

For

x^{2} = f (a)

the solutions are

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

u = \frac{3}{2}, u = - \frac{3}{2}

Substitute back

u = cos (x)

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

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

cos (x) = \frac{3}{2} :

No Solution

cos (x) = \frac{3}{2}

- 1 \leq cos (x) \leq 1

No Solution

cos (x) = - \frac{3}{2} :

No Solution

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

- 1 \leq cos (x) \leq 1

No Solution

Combine all the solutions

No Solution for x \in R

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sin (8 x + 48) = cos (- 4 x + 26)

3 cos (x) + sec (14 5^{\circ}) = 1

sec^{2} (x) + 3 tan^{2} (x) = 13

What is the general solution for cos^2(x)= 3/2 ?
The general solution for cos^2(x)= 3/2 is No Solution for x\in\mathbb{R}