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Chapter 6: Problem 40

Find the exact value of the expression. $$\frac{\tan 25^{\circ}+\tan 110^{\circ}}{1-\tan 25^{\circ} \tan 110^{\circ}}$$

Short Answer

Expert verified
The exact value of the expression is -1.

Step by step solution

01

Recognize the formula

Notice that the expression \(\frac{\tan A + \tan B}{1 - \tan A \tan B}\) equals to \(\tan (A + B)\). In this case, \(A = 25^{\circ}\) and \(B = 110^{\circ}\).
02

Substitute the values

Substitute the values of A and B into the \(\tan (A + B)\) formula. So it becomes \(\tan (25^{\circ} + 110^{\circ})\).
03

Solve the expression

Perform the angle addition to get \(\tan (135^{\circ})\). The value of \(\tan (135^{\circ})\) is -1.

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