Problem 42
Question
In Exercises \(37-42,\) find the exact value of the expression. $$ \frac{\tan 25^{\circ}+\tan 110^{\circ}}{1-\tan 25^{\circ} \tan 110^{\circ}} $$
Step-by-Step Solution
Verified Answer
-1
1Step 1: Identify the Formula
Identify the problem as an application of the formula \( \tan (A + B) = \frac{\tan A + \tan B}{1 - \tan A \tan B}\). Here \(A = 25^\circ\) and \(B = 110^\circ\). The formula simplifies the expression given in the problem.
2Step 2: Substitute
Substitute \( A = 25^\circ\) and \(B = 110^\circ\) into the formula. The resulting expression would be \( \tan (25^\circ + 110^\circ)\).
3Step 3: Compute the Value
The value is \( \tan (135^\circ)\). Depending on the unit circle or the calculator in degrees mode, \( \tan (135^\circ) = -1 \).
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