Question

If $\cosech\,x = \dfrac{4}{5}$, then $\sinh x = $ ?

• A. $\dfrac{4}{5}$
• B. $\dfrac{5}{4}$
• C. $\dfrac{2}{3}$
• D. $\dfrac{2}{5}$

Hint:

Inverse hyperbolic identities are reciprocal — $\cosech x = \frac{1}{\sinh x}$.

Answer 1

The Correct Option is B

By definition: \[ \cosech\,x = \frac{1}{\sinh x} \Rightarrow \sinh x = \frac{1}{\cosech\,x} = \frac{1}{4/5} = \frac{5}{4} \]