Question

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

• A. True
• B. False

Answer 1

The correct option is A True

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

Slope of cosine function $=f^{\prime }\left(\cosh x\right)=\frac{e^x-e^{-x}}{2}........\left(1\right)$

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

From (1) and (2) we have

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

Hence statement is true.