7.
$$\mathrm { f } ( x ) = 5 \cosh x - 4 \sinh x , \quad x \in \mathbb { R }$$
- Show that \(\mathrm { f } ( x ) = \frac { 1 } { 2 } \left( \mathrm { e } ^ { x } + 9 \mathrm { e } ^ { - x } \right)\)
Hence
- solve \(\mathrm { f } ( x ) = 5\)
- show that \(\int _ { \frac { 1 } { 2 } \ln 3 } ^ { \ln 3 } \frac { 1 } { 5 \cosh x - 4 \sinh x } \mathrm {~d} x = \frac { \pi } { 18 }\)