Proof of a trigonometric expression Let $f(x) = (\sin \frac{πx}{7})^{-1}$. Prove that $f(3) + f(2) = f(1)$.
This is another trig question, which I cannot get how to start with. Sum to product identities also did not work.


consider regular 7-gon. applying Ptolemy theorem for $\square ABCD$,
we get $BD\cdot AC=AB\cdot CD+AD\cdot BC$
$BC=AC=2R\sin\dfrac{3\pi}{7}$ , $~BD=CD=2R\sin\dfrac{2\pi}{7}$ , $~AB=AD=2R\sin\dfrac{\pi}{7}$
we're done, where $R$ is the circumradius of regular 7-gon.
