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Chapter 5: Problem 42

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 given trigonometric expression is -1.

Step by step solution

01

Identify the formula

Identify that the given expression falls under the formula tan(A + B), where tan(A + B) = (tanA + tanB) / (1 - tanA*tanB).
02

Identify the values of A and B

From the exercise, it can be observed that \(A = 25^{\circ}\) and \(B = 110^{\circ}\). So plug these values into the formula.
03

Evaluate the expression

Now the formula tan(A + B) becomes tan(135^{\circ}). The standard value of tan(135^{\circ}) can be obtained from the trigonometric table, and it is -1.

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