Question

The value of sun the sum $S=\cot {10}^o$ + $\cot {20}^o$ .....+ $\cot {160}^o$+$\cos {170}^o$ is

Answer 1

$S=(\cot {10}^o+\cot {170}^o)+(\cot {20}^o+\cot {160}^o)+...+(\cot {80}^o+\cot {100}^o)+\cot {90}^o$

$\cot {10}^o=\cot ({180}^o-{170}^o)=-cot{170}^o$

$⟹\cot {10}^0+\cot {170}^o=0$

And similarly for all, and $\cot {90}^o=0$

Hence , $S=0$