Carlos's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Carlos $4.05 per pound, and type B coffee costs $5.40 per pound. This month's blend used four times as many pounds of type B coffee as type A, for a total cost of $923.40. How many pounds of type A coffee were used?

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) = .