Question

The value of ${\log }_{10}\tan {40}^{\circ }{\log }_{10}\tan {41}^{\circ }....{\log }_{10}\tan {50}^{\circ }$ is equal to

Answer 1

We have ${\log }_{10}\tan {45}^{\circ }={\log }_{10}1=0.$
Since ${\log }_{10}\tan {45}^{\circ }$ is one of the factors. of the product, we get
${\log }_{10}\tan {40}^{\circ }{\log }_{10}\tan {41}^{\circ }...{\log }_{10}\mathrm{1..}{\log }_{10}\tan {50}^{\circ }=0,[\because \log 1=0]$

Ans: 0