- (a) Use the definitions of hyperbolic functions in terms of exponentials to show that
$$\sinh ( A + B ) \equiv \sinh A \cosh B + \cosh A \sinh B$$
(b) Hence express \(10 \sinh x + 8 \cosh x\) in the form \(R \sinh ( x + \alpha )\) where \(R > 0\), giving \(\alpha\) in the form \(\ln p\) where \(p\) is an integer.
(c) Hence solve the equation
$$10 \sinh x + 8 \cosh x = 18 \sqrt { 7 }$$
giving your answer in the form \(\ln ( \sqrt { 7 } + q )\) where \(q\) is a rational number to be determined.