What is the general solution for sinh(x-1)=0 ?

The general solution for sinh(x-1)=0 is x=1

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sinh(x-1)=0

Solution

sinh (x - 1) = 0

Solution

x = 1

Degrees

x = 57.29577 \dots^{\circ}

Solution steps

sinh (x - 1) = 0

Rewrite using trig identities

sinh (x - 1) = 0

Use the Hyperbolic identity:

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

\frac{e ^{x - 1} - e ^{- (x - 1)}}{2} = 0

\frac{e ^{x - 1} - e ^{- (x - 1)}}{2} = 0

\frac{e ^{x - 1} - e ^{- (x - 1)}}{2} = 0 : x = 1

\frac{e ^{x - 1} - e ^{- (x - 1)}}{2} = 0

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

e^{x - 1} - e^{- (x - 1)} = 0

Add

e^{- (x - 1)}

to both sides

e^{x - 1} - e^{- (x - 1)} + e^{- (x - 1)} = 0 + e^{- (x - 1)}

Simplify

e^{x - 1} = e^{- (x - 1)}

Apply exponent rules

e^{x - 1} = e^{- (x - 1)}

a^{f (x)} = a^{g (x)}

, then

f (x) = g (x)

x - 1 = - (x - 1)

x - 1 = - (x - 1)

Solve

x - 1 = - (x - 1) : x = 1

x - 1 = - (x - 1)

Expand

- (x - 1) : - x + 1

- (x - 1)

Distribute parentheses

= - (x) - (- 1)

Apply minus-plus rules

- (- a) = a, - (a) = - a

= - x + 1

x - 1 = - x + 1

Move

1

to the right side

x - 1 = - x + 1

Add

1

to both sides

x - 1 + 1 = - x + 1 + 1

Simplify

x = - x + 2

x = - x + 2

Move

x

to the left side

x = - x + 2

Add

x

to both sides

x + x = - x + 2 + x

Simplify

2 x = 2

2 x = 2

Divide both sides by

2

2 x = 2

Divide both sides by

2

\frac{2 x}{2} = \frac{2}{2}

Simplify

x = 1

x = 1

x = 1

x = 1

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Frequently Asked Questions (FAQ)

What is the general solution for sinh(x-1)=0 ?
The general solution for sinh(x-1)=0 is x=1