- (a) Use the definitions of \(\sinh x\) and \(\cosh x\) in terms of exponentials to show that
$$\cosh A \cosh B + \sinh A \sinh B \equiv \cosh ( A + B )$$
(b) Hence find the value of \(x\) for which
$$\cosh ( x + \ln 2 ) = 5 \sinh x$$
giving your answer in the form \(\frac { 1 } { 2 } \ln k\), where \(k\) is a rational number to be determined.
(5)