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.
Solution:
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 $\frac{tan60^o-tan30^o}{1+tan60^o.tan30^o} = tan(60^o − 30^o)$
$= tan(30^o)$
$=\frac{1}{\sqrt{3}}$
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