The first term in this sequence is -1. Which function represents a recursive definition of the sequence? Question 6 options:

a)

an=an−1+1an=an-1+1

b)

an=an−1+2an=an-1+2

c)

an=an−1−1an=an-1-1

d)

an=an−1−3

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) = .