What is the general solution for 8sec^2(x/2)=4 ?

The general solution for 8sec^2(x/2)=4 is No Solution for x\in\mathbb{R}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

8sec^2(x/2)=4

8 sec^{2} (\frac{x}{2}) = 4

No Solution for x \in R

Solution steps

8 sec^{2} (\frac{x}{2}) = 4

Solve by substitution

8 sec^{2} (\frac{x}{2}) = 4

Let:

sec (\frac{x}{2}) = u

8 u^{2} = 4

8 u^{2} = 4 : u = \frac{1}{2}, u = - \frac{1}{2}

8 u^{2} = 4

Divide both sides by

8

8 u^{2} = 4

Divide both sides by

8

\frac{8 u ^{2}}{8} = \frac{4}{8}

Simplify

u^{2} = \frac{1}{2}

u^{2} = \frac{1}{2}

For

x^{2} = f (a)

the solutions are

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

u = \frac{1}{2}, u = - \frac{1}{2}

Substitute back

u = sec (\frac{x}{2})

sec (\frac{x}{2}) = \frac{1}{2}, sec (\frac{x}{2}) = - \frac{1}{2}

sec (\frac{x}{2}) = \frac{1}{2}, sec (\frac{x}{2}) = - \frac{1}{2}

sec (\frac{x}{2}) = \frac{1}{2} :

No Solution

sec (\frac{x}{2}) = \frac{1}{2}

sec (x) \leq - 1 or sec (x) \geq 1

No Solution

sec (\frac{x}{2}) = - \frac{1}{2} :

No Solution

sec (\frac{x}{2}) = - \frac{1}{2}

sec (x) \leq - 1 or sec (x) \geq 1

No Solution

Combine all the solutions

No Solution for x \in R

6 cos^{2} (x) + cos (x) = 1

4 sin (x) + 3 cos (x) = 0

y, x = 2 sin (y)

2 sin (2 x) + 2 sin (x) = 1 + 2 cos (x)

3 sin (x) + 2 = 0

What is the general solution for 8sec^2(x/2)=4 ?
The general solution for 8sec^2(x/2)=4 is No Solution for x\in\mathbb{R}