P is a function that gives the cost, in dollars, of mailing a letter from the Untied States to Mexico in 2018 based on the weight of the letter in ounces, w. The function is defined by this set of rules:

How much does it cost to send a letter that weighs 1.5 ounces?

Prove (a) cosh2(x) − sinh2(x) = 1 and (b) 1 − tanh 2(x) = sech 2(x). solution (a) cosh2(x) − sinh2(x) = ex + e−x 2 2 − 2 = e2x + 2 + e−2x 4 − = 4 = . (b) we start with the identity proved in part (a): cosh2(x) − sinh2(x) = 1. if we divide both sides by cosh2(x), we get 1 − sinh2(x) cosh2(x) = 1 or 1 − tanh 2(x) = .