What is the general solution for sinh^2(x)=0 ?

The general solution for sinh^2(x)=0 is x=0

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sinh^2(x)=0

sinh^{2} (x) = 0

x = 0

Degrees

x = 0^{\circ}

Solution steps

sinh^{2} (x) = 0

Rewrite using trig identities

sinh^{2} (x) = 0

Use the Hyperbolic identity:

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

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

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

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

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

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

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

e^{x} - e^{- x} = 0

Add

e^{- x}

to both sides

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

Simplify

e^{x} = e^{- x}

Apply exponent rules

e^{x} = e^{- x}

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

, then

f (x) = g (x)

x = - x

x = - x

Solve

x = - x : x = 0

x = - x

Move

x

to the left side

x = - x

Add

x

to both sides

x + x = - x + x

Simplify

2 x = 0

2 x = 0

Divide both sides by

2

2 x = 0

Divide both sides by

2

\frac{2 x}{2} = \frac{0}{2}

Simplify

x = 0

x = 0

x = 0

x = 0

x = 0

What is the general solution for sinh^2(x)=0 ?
The general solution for sinh^2(x)=0 is x=0