Question 9 - A-Level Maths

It is given that Starting from the exponential definition of the sinh function, show that $\sinh p = r$ $$p = \ln \left( r + \sqrt { r ^ { 2 } + 1 } \right)$$ Staring fr
9
Solve the equation $$\cosh ^ { 2 } x = 2 \sinh x + 16$$ Give your answers in logarithmic form.
[0pt] [4 marks]
The complex numbers $z$ and $w$ are defined by $$\begin{aligned} z & = \cos \frac { \pi } { 4 } + i \sin \frac { \pi } { 4 }
\text { and } \quad w & = \cos \frac { \pi } { 6 } + i \sin \frac { \pi } { 6 } \end{aligned}$$ By evaluating the product $z w$, show that $$\tan \frac { 5 \pi } { 12 } = 2 + \sqrt { 3 }$$