Willy's Lemma

by adityaguharoy, Jan 9, 2017, 3:57 AM

Willy's Lemma
If $a,b,c,d$ be four acute angles such that $a+b=c+d$ and $\frac{\sin(a)}{\sin(b)}=\frac{\sin(c)}{\sin(d)}$ , then we must have the following :
$$\boxed{a=c\text{ and }b=d}$$Proof :
There are many proofs to this :
$\bullet$ Proof using trigonometry
$\bullet$ Proof using geometry
geometry
willy s lemma

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