find the exact value of the expression. (tan 25° + tan 110°)/(1 - tan 25° tan 110°) -1 need help? read it…

Explanation:

Step1: Recall tangent - sum formula

The formula for $\tan(A + B)=\frac{\tan A+\tan B}{1 - \tan A\tan B}$. In the given expression $\frac{\tan25^{\circ}+\tan110^{\circ}}{1 - \tan25^{\circ}\tan110^{\circ}}$, we have $A = 25^{\circ}$ and $B=110^{\circ}$. So, $\frac{\tan25^{\circ}+\tan110^{\circ}}{1 - \tan25^{\circ}\tan110^{\circ}}=\tan(25^{\circ}+110^{\circ})$.

Step2: Calculate the sum of angles

$25^{\circ}+110^{\circ}=135^{\circ}$.

Step3: Find the tangent value

We know that $\tan135^{\circ}=\tan(180^{\circ}- 45^{\circ})$. Since $\tan(180^{\circ}-\alpha)=-\tan\alpha$, then $\tan(180^{\circ}-45^{\circ})=-\tan45^{\circ}$. And $\tan45^{\circ}=1$, so $\tan135^{\circ}=- 1$.

Answer:

$-1$