Given that z = sin(x)/cos(x), use the quoitent rule to show that dZ/dx = sec^2(x)

let u = sin(x) and v = cos(x) => z = u/v. The quoitent rule is (u'v - v'u)/v^2, where u' = du/dx, v' = dv/dx. In this case du/dx = cos(x) and dv/dx = -sin(x) => u'v = cos^2(x) and v'u = -sin^2(x) => u'v - v'u = cos^2(x) + sin^2(x) = 1.v^2 = cos^2(x) => dz/dx = 1/v^2 = 1/cos^2(x) = sec^2(x)