/*
 * spherecurv.maxima
 *
 * (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
 */
f: exp(-a * sin(theta)^2);

g: ratsimp(diff(sin(theta) * diff(f, theta), theta)/sin(theta));
g: subst(z, cos(theta), g);
g: subst(sqrt(1-z^2), sin(theta), g);
ratsimp(g);

f: ratsimp(subst(sqrt(1-z^2), sin(theta), f));