Lan is buying a house. The floor plan is drawn with a scale of 1/2 inch represents 1 foot. lan measured the dimensions on the floor plan with a ruler. He found that the master bedroom has
a width of 1.5 inches and a length of 3.75 inches. What is the actual width of the room?

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) = .