Do the following:

a. Write \((\cosh x-\sinh x)^{6}\) in terms of exponentials.

b. Prove \(\cosh (x-y)=\cosh x \cosh y-\sinh x \sinh y\) using the exponential forms of the hyperbolic functions.

c. Prove \(\cosh 2 x=\cosh ^{2} x+\sinh ^{2} x\).

d. If \(\cosh x=\frac{13}{12}\) and \(x<0\), find \(\sinh x\) and \(\tanh x\).

e. Find the exact value of \(\sinh (\operatorname{arccosh} 3)\).