Answer
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 $1$.
Work Step by Step
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 $1$.
