What is the general solution for sinh(x)= 1/2 ?

The general solution for sinh(x)= 1/2 is x=ln((1+sqrt(5))/2)

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sinh(x)= 1/2

sinh (x) = \frac{1}{2}

x = ln (\frac{1 + 5}{2})

Solution steps

sinh (x) = \frac{1}{2}

Rewrite using trig identities

\frac{e ^{x} - e ^{- x}}{2} = \frac{1}{2}

\frac{e ^{x} - e ^{- x}}{2} = \frac{1}{2} : x = ln (\frac{1 + 5}{2})

x = ln (\frac{1 + 5}{2})

sin^{2} (x) \cdot sec (x) = \frac{sin ^{2} ( x )}{cot ( x )}

2 tan (θ) + sin (θ) cos (θ) = 0

sec (x) = \frac{25}{7}

sin (\frac{x}{2}) = \frac{1}{2} sin (x)

tan (θ) = \frac{- 3}{3}

What is the general solution for sinh(x)= 1/2 ?
The general solution for sinh(x)= 1/2 is x=ln((1+sqrt(5))/2)