Question

cot pi/20 cot 3pi/20 cot5pi/20 cot7pi/20 cot9pi/20=1

Answer 1

The given expression is $cot \frac{π}{20}cot \frac{3π}{20}cot \frac{5π}{20}cot \frac{7π}{20}cot \frac{9π}{20}$,

which can be written as

$cot( \frac{π}{20})cot( \frac{3π}{20})cot( \frac{5π}{20}) cot( \frac{π}{2} - \frac{3π}{20})cot( \frac{π}{2} - \frac{π}{20})$

$= [tex]= cot \frac{5π}{20} = cot \frac{π}{4} = 1$cot( \frac{π}{20})cot( \frac{3π}{20})cot( \frac{5π}{20})tan( \frac{π}{20})tan( \frac{3π}{20})[/tex]