Find the value of $\frac{tan60^o-tan30^o}{1+tan60^o\times tan30^o}$.

Given: $\frac{tan60^o-tan30^o}{1+tan60^o\times tan30^o}$

To do: To find the value of given expression.

As given $\frac{tan60^o-tan30^o}{1+tan60^o.tan30^o}$

It is in the form of $\frac{( tanA -  tanB)}{( 1+ tanA.tanB)}$ which is equal to $tan( A - B)$

Hence  $\frac{tan60^o-tan30^o}{1+tan60^o.tan30^o} = tan(60^o − 30^o)$

                                    $= tan(30^o)$

                                    $=\frac{1}{\sqrt{3}}$