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

The general solution for sinh(ax)=0 is x=0

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sinh(ax)=0

sinh (a x) = 0

x = 0

Degrees

x = 0^{\circ}

Solution steps

sinh (a x) = 0

Rewrite using trig identities

sinh (a x) = 0

Use the Hyperbolic identity:

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

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

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

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

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

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

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

Add

e^{- a x}

to both sides

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

Simplify

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

Apply exponent rules

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

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

, then

f (x) = g (x)

a x = - a x

a x = - a x

Solve

a x = - a x : x = 0

a x = - a x

Move

a x

to the left side

a x = - a x

Add

a x

to both sides

a x + a x = - a x + a x

Simplify

2 a x = 0

2 a x = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0

x = 0

x = 0

8 sin^{4} (x) - 3 sin^{2} (x) + \frac{1}{4} = 0

- 2 cot (θ) = - 1 - cot^{2} (θ)

- cos^{2} (x) - sin (x) - 1 = 0

- 8 cos^{2} (x) + 1 = 4 sin^{2} (x) - 8 cos (x)

\frac{1 + csc ( y )}{cot ( y ) + cos ( y )} = csc (y)

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