Question

What is the value of ${\left[\frac{\cos {10}^0+\sin {20}^0}{\cos {20}^0-\sin {10}^0}\right]}^2$?

Answer 1

${\left[\frac{\cos 10+\sin 20}{\cos 20-\sin 10}\right]}^2$

${\left[\frac{\cos (90-80)+\sin 20}{\cos 20-\sin (90-80)}\right]}^2$

${\left[\frac{\sin 80+\sin 20}{\cos 20-\cos 80}\right]}^2$

${\left[\frac{2\sin \left(\frac{80+20}{2}\right)\cos \left(\frac{80-20}{2}\right)}{2\sin \left(\frac{80+20}{2}\right)\sin \left(\frac{80-20}{2}\right)}\right]}^2$

${\cot }^{2}30=3$