What is the general solution for sinh(x)= 5/12 ?

The general solution for sinh(x)= 5/12 is x=ln(3/2)

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sinh(x)= 5/12

sinh (x) = \frac{5}{12}

x = ln (\frac{3}{2})

Solution steps

sinh (x) = \frac{5}{12}

Rewrite using trig identities

\frac{e ^{x} - e ^{- x}}{2} = \frac{5}{12}

\frac{e ^{x} - e ^{- x}}{2} = \frac{5}{12} : x = ln (\frac{3}{2})

x = ln (\frac{3}{2})

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

10 sin (x) + 1 = 3 - 2 sin (x)

2 cos (x) - 9 = - 4 sec (x)

2 sin (θ) + 4 = 4

4 sin^{2} (x) + (23 + 2) sin (x) + 3 = 0

What is the general solution for sinh(x)= 5/12 ?
The general solution for sinh(x)= 5/12 is x=ln(3/2)