Question

use the sum and difference identities to rewrite the following expression as a trigonometric function of one angle.
\frac{\tan(70^{circ})+\tan(25^{circ})}{1 - \tan(70^{circ})\tan(25^{circ})}

Explanation:

Step1: Recall tangent sum - identity

The tangent sum - identity is $\tan(A + B)=\frac{\tan A+\tan B}{1 - \tan A\tan B}$.

Step2: Identify A and B

In the given expression $\frac{\tan(70^{\circ})+\tan(25^{\circ})}{1 - \tan(70^{\circ})\tan(25^{\circ})}$, we have $A = 70^{\circ}$ and $B=25^{\circ}$.

Step3: Apply the identity

By substituting $A = 70^{\circ}$ and $B = 25^{\circ}$ into the tangent sum - identity, we get $\tan(70^{\circ}+25^{\circ})$.

Answer:

$\tan(95^{\circ})$