Question

Write the expression as either the sine, cosine, or tangent of a single angle. tan5x - tan2y / 1 + tan5x tan2y

Answer 1

$\bf \textit{Sum and Difference Identities} \\\\ tan(\alpha + \beta) = \cfrac{tan(\alpha)+ tan(\beta)}{1- tan(\alpha)tan(\beta)} \qquad tan(\alpha - \beta) = \cfrac{tan(\alpha)- tan(\beta)}{1+ tan(\alpha)tan(\beta)}\\\\ -------------------------------\\\\ \cfrac{tan(5x)-tan(2y)}{1+tan(5x)tan(2y)}\implies tan(5x-2y)$