What is the general solution for cosh((zz)/2)=0 ?

The general solution for cosh((zz)/2)=0 is No Solution for z\in\mathbb{R}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cosh((zz)/2)=0

cosh (\frac{zz}{2}) = 0

No Solution for z \in R

Solution steps

cosh (\frac{zz}{2}) = 0

Rewrite using trig identities

cosh (\frac{zz}{2}) = 0

Use the Hyperbolic identity:

cosh (x) = \frac{e ^{x} + e ^{- x}}{2}

\frac{e ^{\frac{zz}{2}} + e ^{- \frac{zz}{2}}}{2} = 0

\frac{e ^{\frac{zz}{2}} + e ^{- \frac{zz}{2}}}{2} = 0

\frac{e ^{\frac{zz}{2}} + e ^{- \frac{zz}{2}}}{2} = 0 : z = Undefined, z = - Undefined

\frac{e ^{\frac{zz}{2}} + e ^{- \frac{zz}{2}}}{2} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

e^{\frac{zz}{2}} + e^{- \frac{zz}{2}} = 0

Subtract

e^{- \frac{zz}{2}}

from both sides

e^{\frac{zz}{2}} + e^{- \frac{zz}{2}} - e^{- \frac{zz}{2}} = 0 - e^{- \frac{zz}{2}}

Simplify

e^{\frac{zz}{2}} = - e^{- \frac{zz}{2}}

Apply exponent rules

e^{\frac{zz}{2}} = - e^{- \frac{zz}{2}}

f (x) = g (x)

, then

ln (f (x)) = ln (g (x))

ln (e^{\frac{zz}{2}}) = ln (- e^{- \frac{zz}{2}})

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (- e^{- \frac{zz}{2}}) = ln (- 1) + ln (e^{- \frac{zz}{2}})

ln (e^{\frac{zz}{2}}) = ln (- 1) + ln (e^{- \frac{zz}{2}})

Apply log rule:

ln (e^{a}) = a

ln (e^{\frac{zz}{2}}) = \frac{zz}{2}

\frac{zz}{2} = ln (- 1) + ln (e^{- \frac{zz}{2}})

Apply log rule:

ln (e^{a}) = a

ln (e^{- \frac{zz}{2}}) = - \frac{zz}{2}

\frac{zz}{2} = ln (- 1) - \frac{zz}{2}

\frac{zz}{2} = ln (- 1) - \frac{zz}{2}

Solve

\frac{zz}{2} = ln (- 1) - \frac{zz}{2} : z = Undefined, z = - Undefined

\frac{zz}{2} = ln (- 1) - \frac{zz}{2}

Move

\frac{zz}{2}

to the left side

\frac{zz}{2} = ln (- 1) - \frac{zz}{2}

Add

\frac{zz}{2}

to both sides

\frac{zz}{2} + \frac{zz}{2} = ln (- 1) - \frac{zz}{2} + \frac{zz}{2}

Simplify

z^{2} = ln (- 1)

z^{2} = ln (- 1)

lo g_{a} (b), b < 0

is undefined

z^{2} = Undefined

For

x^{2} = f (a)

the solutions are

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

z = Undefined, z = - Undefined

z = Undefined, z = - Undefined

z = Undefined, z = - Undefined

Since the equation is undefined for:

Undefined, - Undefined

No Solution for z \in R

t, 2 cos (t) = x

cos^{4} (x) = 1 - sin^{4} (x)

2 sinh (x) - 2 cosh (x) - 2 = 0

sec^{2} (x) + cot^{2} (x) = csc^{2} (x)

\frac{sin ( 7 9 ^{\circ} )}{12} = \frac{sin ( B )}{7}

What is the general solution for cosh((zz)/2)=0 ?
The general solution for cosh((zz)/2)=0 is No Solution for z\in\mathbb{R}