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Chapter 5: Problem 39

Find the exact value of the expression. $$\frac{\tan (5 \pi / 6)-\tan (\pi / 6)}{1+\tan (5 \pi / 6) \tan (\pi / 6)}$$

Short Answer

Expert verified
The exact value of the expression is \(0\).

Step by step solution

01

Recognize the identity

Identify that the expression given is in the form of the tangent addition identity for subtraction, i.e., \(\tan(a - b)\). This means that the given expression is equivalent to \(\tan(5\pi/6 - \pi/6)\).
02

Subtract the angles

Subtract the angles inside the tangent function, \(5\pi/6 - \pi/6\) to calculate the angle.
03

Solve for the value of tangent function

Substitute the result from the subtraction, which is the angle, into the function \(\tan(x)\) to find the exact value.

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