Chapter 6.9, Problem 59ES

Prove the identities.

(a) $1-{\tanh }^{2}x={\mathrm{sech}}^{2}x$

(b) $\tanh \left(x+y\right)=\frac{\tanh x+\tanh y}{1+\tanh x\tanh y}$

(c) $\tanh 2x=\frac{2\tanh x}{1+{\tanh }^{2}x}$