Question

The slope of the hyperbolic sine function is equal to the hyperbolic cosine function.State true or false.

• A. True
• B. False

Answer 1

The correct option is A True

$f\left(x\right)=\sinh x=\frac{e^x-e^{-x}}{2}$

Slope of sine function = $f^{\prime }\left(x\right)=\frac{d}{dx}\frac{e^x-e^{-x}}{2}$

$=\frac{e^x+e^{-x}}{2}..............\left(1\right)$

and $\cosh x=\frac{e^x+e^{-x}}{2}...........\left(2\right)$

From (1) and (2)

$f^{\prime }\left(x\right)=\cosh x$

Hence statement is true.