[Solved] Find The Value Of Sinh (ln 4).

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Concept:

The exponential representation of the basic hyperbolic functions are:

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

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

n.ln (m) = ln(m)n

eln(x) = x

Calculation:

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

Put x = ln 4

\(⇒ sin h(ln\ 4) = \frac{e^{ln {4}}-e^{-ln{4}}}{2}\)

\(⇒ sin h(ln\ 4) = \frac{e^{ln {(4)}}-e^{ln{(4)^{-1}}}}{2}\)

Since, n.ln (m) = ln(m)n

\(⇒ sinh (ln \ 4) = \frac{4 \ - \ 4^{-1}}{2}\)

\(⇒ \frac{\frac{16 - 1}{4}} {2}\)

⇒ 15/8

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