EXAMPLE:
If X= \[ {60}^{\circ}\] and Y= \[ {30}^{\circ}\] ,then prove that tan(x-y)=\[\frac{tanx-tany}{1+tanx\times tany}\]
LHS =
tan(x-y)=tan( \[ {60}^{\circ}\] - \[ {30}^{\circ}\]) = tan\[ {30}^{\circ}\] = \[\frac{1}{\sqrt{3}}\] = 0.57735
RHS=
tanx-tany= tan\[ {60}^{\circ}\] - tan\[ {30}^{\circ}\] = ( \[\sqrt{3}\] - \[\frac{1}{\sqrt{3}}\]) = \[\frac{3-1}{\sqrt{3}}\] =\[\frac{2}{\sqrt{3}}\] (equation 1)
1+ tanx tany= 1+ tan\[ {60}^{\circ}\] tan\[ {30}^{\circ}\] = 1+(\[\sqrt{3}\] \[\frac{1}{\sqrt{3}}\] )= 1+1 =2 (equation 2)
RHS=\[\frac{equation 1}{equation 2}\] =\[\frac{\frac{2}{\sqrt{3}}}{2}\] = \[\frac{1}{\sqrt{3}}\] = 0.57735
\[\therefore \] LHS =RHS
