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.
-$\cosh x = \frac { 13 } { 12 } , x 0 , \tanh x =$
A) $\frac { 5 } { 13 }$
B) $- \frac { 25 } { 144 }$
C) $\frac { 5 } { 12 }$
D) $\frac { 13 } { 5 }$

Question

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.
-$\cosh x = \frac { 13 } { 12 } , x > 0 , \tanh x =$
A) $\frac { 5 } { 13 }$
B) $- \frac { 25 } { 144 }$
C) $\frac { 5 } { 12 }$
D) $\frac { 13 } { 5 }$

Quizplus · Accepted Answer

Given $\cosh x = \frac{13}{12}$, we use the identity $\cosh^2 x - \sinh^2 x = 1$ to find $\sinh x$, then calculate $\tanh x = \frac{\sinh x}{\cosh x}$. Solving for $\sinh x$ gives $\sinh x = \frac{5}{12}$ for $x > 0$, thus $\tanh x = \frac{5}{13}$.

A Value of Sinh X or Cosh X Is Given cosh⁡x=1312,x>0,tanh⁡x=\cosh x = \frac { 13 } { 12 } , x > 0 , \tanh x =coshx=1213​,x>0,tanhx=

A Value of Sinh X or Cosh X Is Given $\cosh x = \frac { 13 } { 12 } , x > 0 , \tanh x =$