The following is a generalization of the half-angle formulas presented at Nabla - Applications of Trigonometry.

**Generalization**. Let $a$, $b$, $c$, $d$ be the sides of a general convex quadrilateral, $s$ is the semiperimeter, and $\alpha$ and $\gamma$ are opposite angles, then
$$ad\sin^2{\frac{\alpha}{2}}+bc\cos^2{\frac{\gamma}{2}}=(s-a)(s-d)\qquad\qquad bc\sin^2{\frac{\gamma}{2}}+ad\cos^2{\frac{\alpha}{2}}=(s-b)(s-c).\tag{1}$$
I am interested in the following:
**a)** If possible, a spherical generalization of $(1)$.
**b)** If **a)** is answered in the affirmative, what classical metric relations of spherical trigonometry would follows from **a)** (or a particular case of a)?

This question is related to a previous question.

Crossposted at MathSE