Basic hyperbolic identitiesAQA A-Level Further Maths: Mind map

Exam questions on Basic hyperbolic identities

1. A real number $x$ satisfies $\sinh x=\frac34$.
   Find the exact value of $\cosh^2x+\sinh^2x$.2 marks
2. A real number $x>0$ satisfies $\tanh x=\frac45$.
   Hence find the exact value of $x$.2 marks
3. Hyperbolic functions are defined by $\cosh x=\frac12(e^x+e^{-x})$ and $\sinh x=\frac12(e^x-e^{-x})$.
   Prove that $\cosh^2x-\sinh^2x=1$ for all real $x$.3 marks