Question

Simplify the following expressions.
$logtan{3}^{\circ }\cdot logtan{6}^{\circ }\cdot logtan{9}^{\circ }.......logtan{87}^{\circ }$

Answer 1

$\log \tan 3^o.\log \tan 6^o...\log \tan {45}^o...\log \tan {87}^o$

$=\log \tan 3^o.\log \tan 6^o...\log 1...\log \tan {87}^o$

$=\log \tan 3^o.\log \tan 6^o...\times \mathrm{0...}\log \tan {87}^o$

$=0$