Which of the following is the reciprocal of:
x^2 - 2x - 8
a.
(x + 2)(x-4)
b.
1/
(x - 8)
c.
1 /
(x + 2)(x - 4)
d.
1 /
(x + 2)

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) = .