What is the general solution for 2cos^2(x)-3=0 ?

The general solution for 2cos^2(x)-3=0 is No Solution for x\in\mathbb{R}

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2cos^2(x)-3=0

2 cos^{2} (x) - 3 = 0

No Solution for x \in R

Solution steps

2 cos^{2} (x) - 3 = 0

Solve by substitution

2 cos^{2} (x) - 3 = 0

Let:

cos (x) = u

2 u^{2} - 3 = 0

2 u^{2} - 3 = 0 : u = \frac{3}{2}, u = - \frac{3}{2}

2 u^{2} - 3 = 0

Move

3

to the right side

2 u^{2} - 3 = 0

Add

3

to both sides

2 u^{2} - 3 + 3 = 0 + 3

Simplify

2 u^{2} = 3

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

2 sin (x) + 3 tan (x) = 0

tan (t) = 2, 0 < t < \frac{π}{2}, cos (t)

\frac{cos ( x ) + sin ( x )}{sin ( x )} = \frac{1}{tan ( x )}

cos (2 x) - 3 sin (- x) - 2 = 0

sin (θ) = \frac{1}{4}, 0 < θ < \frac{π}{2}

What is the general solution for 2cos^2(x)-3=0 ?
The general solution for 2cos^2(x)-3=0 is No Solution for x\in\mathbb{R}