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

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

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sinh(2x)=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 ^{2 x} - e ^{- 2 x}}{2} = 0

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

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

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

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

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

Add

e^{- 2 x}

to both sides

e^{2 x} - e^{- 2 x} + e^{- 2 x} = 0 + e^{- 2 x}

Simplify

e^{2 x} = e^{- 2 x}

Apply exponent rules

e^{2 x} = e^{- 2 x}

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

, then

f (x) = g (x)

2 x = - 2 x

2 x = - 2 x

Solve

2 x = - 2 x : x = 0

2 x = - 2 x

Move

2 x

to the left side

2 x = - 2 x

Add

2 x

to both sides

2 x + 2 x = - 2 x + 2 x

Simplify

4 x = 0

4 x = 0

Divide both sides by

4

4 x = 0

Divide both sides by

4

\frac{4 x}{4} = \frac{0}{4}

Simplify

x = 0

x = 0

x = 0

x = 0

cos^{2} (x) = \frac{1}{2} + \frac{1}{2} cos^{2} (x)

3 tan (x) = \frac{1}{cos ( x )}

cos (x) - sin (x) = 0, - π \leq x \leq π

5 - tan^{2} (x) = 4

2 sec^{2} (θ) - 3 = tan^{2} (θ)

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