Further hyperbolic identities and proofsAQA A-Level Further Maths: Mind map

Exam questions on Further hyperbolic identities and proofs

1. Given that $\tanh x=\frac{3}{5}$ and $x>0$.
   Find the exact value of $\sinh 2x$.2 marks
2. Given that $\coth x=\frac{5}{4}$ and $x>0$.
   Find the exact value of $\cosh 2x$.2 marks
3. You may assume $\cosh^2x-\sinh^2x=1$ and $\cosh 2x=\cosh^2x+\sinh^2x$.
   Show that $\cosh 2x\equiv1+2\sinh^2x$.3 marks