Chapter 6, Problem 25RE

In each part, prove the identity.

(a) $\cosh 3x=4{\cosh }^{3}x-3\cosh x$

(b) $\cosh \frac{1}{2}x=\sqrt{\frac{1}{2}\left(\cosh x+1\right)}$

(c) $\sinh \frac{1}{2}x=\pm \sqrt{\frac{1}{2}\left(\cosh x-1\right)}$