Inverse hyperbolic functionsAQA A-Level Further Maths: Mind map

Exam questions on Inverse hyperbolic functions

1. Let $a=\sinh^{-1}\left(\frac34\right)$ and $b=\tanh^{-1}\left(\frac12\right)$.
   Express $a+2b$ as a single natural logarithm.2 marks
2. Let $c=\cosh^{-1}\left(\frac53\right)$.
   Solve $\cosh x=\frac53$.2 marks
3. A student sets $y=\sinh^{-1}x$ for a real number $x$, so that $x=\sinh y$.
   Show that $y=\ln\left(x+\sqrt{x^2+1}\right)$.3 marks