1. The problem statement, all variables and given/known data x=sec(t), y=tan(t), -π/2 ≤ t ≤ π/2 Try to find y in terms of x 2. Relevant equations 3. The attempt at a solution 1. ∂y/∂x = sec(t)/tan(t) y=∫sec(t)/tan(t)∂x =∫x/y∂x =(1/y)*∫x∂x =x2/2y + C 2y2=x2 + C When t=π/4, x=√2, y=1 2(1)2 = (√2)2 + C C=0 So y2 = x2/2 2. y/x = sin(t) 1/x = cos(t) sin2(t) + cos2(t) = 1 y2/x2 + 1/x2 = 1 y2 = x2 + 1 Why couldn't I get the same equations in both (1) and (2)? It turns out only the equation 2 works well with other value of t. What did I do wrong in (1)?