Rectangular equation for the curve whose parametric equations are x = 2cosθ, y = cos2θ.

What can you determine about the solutions of this system

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) = .

The following numbers will result in a quotient that is less than 1 when it is divided by ? a.2% e. 1 and 2/3 b.x2 f. 1/5 c. 3/10 g. 7/15 d. 5/9