What is the general solution for sinh(y)=0 ?

The general solution for sinh(y)=0 is y=0

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sinh(y)=0

sinh (y) = 0

y = 0

Degrees

y = 0^{\circ}

Solution steps

sinh (y) = 0

Rewrite using trig identities

sinh (y) = 0

Use the Hyperbolic identity:

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

\frac{e ^{y} - e ^{- y}}{2} = 0

\frac{e ^{y} - e ^{- y}}{2} = 0

\frac{e ^{y} - e ^{- y}}{2} = 0 : y = 0

\frac{e ^{y} - e ^{- y}}{2} = 0

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

e^{y} - e^{- y} = 0

Add

e^{- y}

to both sides

e^{y} - e^{- y} + e^{- y} = 0 + e^{- y}

Simplify

e^{y} = e^{- y}

Apply exponent rules

e^{y} = e^{- y}

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

, then

f (x) = g (x)

y = - y

y = - y

Solve

y = - y : y = 0

y = - y

Move

y

to the left side

y = - y

Add

y

to both sides

y + y = - y + y

Simplify

2 y = 0

2 y = 0

Divide both sides by

2

2 y = 0

Divide both sides by

2

\frac{2 y}{2} = \frac{0}{2}

Simplify

y = 0

y = 0

y = 0

y = 0

What is the general solution for sinh(y)=0 ?
The general solution for sinh(y)=0 is y=0