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

= - x - 1

x + 1 = - x - 1

Move

1

to the right side

x + 1 = - x - 1

Subtract

1

from 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

Popular Examples

sin(a)=0.6542

sin (a) = 0.6542

0=-6sin(3x)

0 = - 6 sin (3 x)

tan(x)=4-3cot(x)

tan (x) = 4 - 3 cot (x)

tan(x)=193.661

tan (x) = 193.661

sin(θ)=0.242

sin (θ) = 0.242

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