How can the trigonometric equation be proven? This question :
https://math.stackexchange.com/questions/1411700/whats-the-size-of-the-x-angle
has the answer $10°$. This follows from the equation
$$2\sin(80°)=\frac{\sin(60°)}{\sin(100°)}\times \frac{\sin(50°)}{\sin(20°)}$$
which is indeed true , which I checked with Wolfram.


*

*How can this equation be proven ?


$$
2\cdot\sin80^\circ\cdot \underbrace{\sin100^\circ}_{\sin80^\circ}\cdot\sin20^\circ=2\cdot \sin80^\circ\cdot2\sin40^\circ\underbrace{\cos40^\circ}_{\sin50^\circ}\cdot\sin20^\circ=\\
=\underbrace{4\cdot\sin80^\circ\cdot\sin40^\circ\cdot\sin20^\circ}_{\sqrt{3}/2}\cdot\sin50^\circ=\sin60^\circ\cdot\sin50^\circ.
$$
The only non-obvious identity is Morrie's law for sine.
