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

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

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2cos^2(x)=3

2 cos^{2} (x) = 3

No Solution for x \in R

Solution steps

2 cos^{2} (x) = 3

Solve by substitution

2 cos^{2} (x) = 3

Let:

cos (x) = u

2 u^{2} = 3

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

2 u^{2} = 3

Divide both sides by

2

2 u^{2} = 3

Divide both sides by

2

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

Simplify

u^{2} = \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

9 tan (2 x) - 9 cot (x) = 0

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

sin (x) sec (x) = sin (x)

cos (x) + 2 = 0

\frac{2 tan ( 3 x )}{1 - tan ^{2} ( 3 x )} = 1

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