Given P(A)=0.8P(A)=0.8, P(B)=0.62P(B)=0.62 and P(A union B)=0.874P(A∪B)=0.874, find the value of P(A unionB)P(A∩B), rounding to the nearest thousandth, if necessary.

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) = .