Question

2. Introduction to Hyperbolic Functions $\sinh x = \frac{e^x - e^{-x}}{2}$ $\cosh x = \frac{e^x + e^{-x}}{2}$ (a) Show that $1 - \tanh^2 x = \sech^2 x$ (b) Hence find the value of $x$ for which $5 \sech^2 x = 11 - 13 \tanh x$ (c) Given that $9 \sinh x - \cosh x = 8$. Show that $\tanh x = \frac{21}{29}$ (d) Find the inverse of $\sinh x$

          2. Introduction to Hyperbolic Functions
$\sinh x = \frac{e^x - e^{-x}}{2}$ 
$\cosh x = \frac{e^x + e^{-x}}{2}$
(a) Show that $1 - \tanh^2 x = \sech^2 x$
(b) Hence find the value of $x$ for which $5 \sech^2 x = 11 - 13 \tanh x$
(c) Given that $9 \sinh x - \cosh x = 8$. Show that $\tanh x = \frac{21}{29}$
(d) Find the inverse of $\sinh x$

2. Introduction to Hyperbolic Functions
sinh x = (e^x - e^-x)/(2)
cosh x = (e^x + e^-x)/(2)
(a) Show that 1 - tanh^2 x = sech^2 x
(b) Hence find the value of x for which 5 sech^2 x = 11 - 13 tanh x
(c) Given that 9 sinh x - cosh x = 8. Show that tanh x = (21)/(29)
(d) Find the inverse of sinh x

Added by Tamara H.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Arpit Giri

03/20/2022

Step 1

Step 1: To show that 1 - tanh^(2)x = sech^(2)x, we start with the definitions of tanh x and sech x: tanh x = sinh x / cosh x sech x = 1 / cosh x Show more…

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Introduction to Hyperbolic Functions sinh x = (e^(x) - e^(-x)) / 2, cosh x = (e^(x) + e^(-x)) / 2 (a) Show that 1 - tanh^(2)x = sech^(2)x (b) Hence find the value of x for which 5sech^(2)x = 11 - 13tanhx (c) Given that 9sinhx - coshx = 8, show that tanhx = 21 / 29 (d) Find the inverse of sinhx 2. Introduction to Hyperbolic Functions sinh x cosh x 2 2 (a) Show that 1 - tanhx = sechx (b) Hence find the value of x for which 5sechx = 11 - 13tanhx (c) Given that 9sinhx - coshx = 8, show that tanhx = 29 (d) Find the inverse of sinhx