A Value Of $\sinh x$ Or $\cosh x$ Is Given Use the Definitions and the Identity

Multiple Choice

A value of $\sinh x$ or $\cosh x$ is given. Use the definitions and the identity $\cosh ^ { 2 } x - \sinh ^ { 2 } x = 1$ to find the value of the other indicated hyperbolic function.
- $\cosh x = \frac { 13 } { 5 } , x < 0 , \operatorname { coth } x =$

A) $- \frac { 12 } { 5 }$
B) $- \frac { 13 } { 12 }$
C) $- \frac { 5 } { 13 }$
D) $\frac { 12 } { 13 }$