## Precalculus (6th Edition) Blitzer

The expression $\frac{\tan 10{}^\circ +\tan 35{}^\circ }{1-\tan 10{}^\circ \tan 35{}^\circ }$ is written as $\tan 45{}^\circ$ and the exact value of $\tan 45{}^\circ$ is $1$.
Use the sum formula of tangent and rewrite the expression as the sum of angles to obtain the tangent of the angle as, \begin{align} & \tan \left( 10{}^\circ +35{}^\circ \right)=\frac{\tan 10{}^\circ +\tan 35{}^\circ }{1-\tan 10{}^\circ \tan 35{}^\circ } \\ & \tan \left( 45{}^\circ \right)=\frac{\tan 10{}^\circ +\tan 35{}^\circ }{1-\tan 10{}^\circ \tan 35{}^\circ } \end{align} Therefore, the expression $\frac{\tan 10{}^\circ +\tan 35{}^\circ }{1-\tan 10{}^\circ \tan 35{}^\circ }$ is equivalent to $\tan 45{}^\circ$. From the knowledge of trigonometric ratios defined for tangent of an angle, the exact value of $\tan 45{}^\circ$ is $1$.