The vertex of this parabola is at (1,3). which of the following could be its
equation?
(1,3) oc
o a. x=3(y - 3)2+1
o b. = 3(y - 3)2-1
o c. y = 3(x + 1)2-3
d. y = 3(x + 1)2 + 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) = .