Question

Solve: $lo{g}_{10}tan{40}^{\circ }lo{g}_{10}tan{41}^{\circ }......lo{g}_{10}tan{50}^{\circ }$

Answer 1

Given:

${\log }_{10}\tan 40°{\log }_{10}\tan 41°.......................{\log }_{10}\tan 50°$

$={\log }_{10}\tan 40°{\log }_{10}\tan 41°{\log }_{10}\tan 42°{\log }_{10}\tan 43°{\log }_{10}\tan 44°{\log }_{10}\tan 45°{\log }_{10}\tan 46°{\log }_{10}\tan 47°{\log }_{10}\tan 48°{\log }_{10}\tan 49°{\log }_{10}\tan 50°$

$=0$ [We know ${\log }_{10}\tan 45°={\log }_{10}1=0$ and anything multiplied to zero is zero]