Question

Write the given expression as the tangent of an angle tan 3x-tan 7x/1+tan3x tan7x

Answer 1

$\bf tan({{ \alpha}} + {{ \beta}}) = \cfrac{tan({{ \alpha}})+ tan({{ \beta}})}{1- tan({{ \alpha}})tan({{ \beta}})}\qquad tan({{ \alpha}} - {{ \beta}}) = \cfrac{tan({{ \alpha}})- tan({{ \beta}})}{1+ tan({{ \alpha}})tan({{ \beta}})}\\\\ -----------------------------\\\\ \cfrac{tan(3x)-tan(7x)}{1+tan(3x)tan(7x)}\implies tan(3x-7x)\implies tan(10x)$