Question

Let $E=\left(1-\frac{\cos 61^{\circ }}{\cos 1^{\circ }}\right)\left(1-\frac{\cos 62^{\circ }}{\cos 2^{\circ }}\right)\dots \left(1-\frac{\cos 119^{\circ }}{\cos 59^{\circ }}\right)$ then $E$ is equal to

Answer 1

Answer: 1

Given $I=\prod _{r=1}^{59}\left(1-\frac{\cos \left(60^{\circ }+r^{\circ }\right)}{\cos r^{\circ }}\right)$
$=\prod _{r=1}^{59}\frac{\sin \left(30^{\circ }+r^{\circ }\right)}{\cos r^{\circ }}$
$=\frac{\sin 31^{\circ }\cdot \sin 32^{\circ }\dots \sin 89^{\circ }}{\cos 1^{\circ }\cdot \cos 2\dots \cos 59^{\circ }}=1$