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Chapter 6: Problem 84

Use words to describe the formula for: the tangent of double an angle.

Short Answer

Expert verified
The tangent of double an angle \(2A\) can be expressed using the formula \(\frac{{2\tan(A)}}{{1-\tan^2(A)}}\). This essentially means twice the tangent of the original angle divided by \(1 -\) the square of the tangent of the original angle.

Step by step solution

01

Identify the formula

The formula for the tangent of double an angle is denoted as \(\tan(2A)\). It is a trigonometric identity expressed in terms of the tangent of the individual angle (A). The formula is:\[\tan(2A) = \frac{{2\tan(A)}}{{1 - \tan^2(A)}}\]
02

Explain the formula

The formula can be explained as follows: The tangent of double an angle (2A), is equivalent to twice the tangent of the original angle (A) divided by \(1 - \) the square of the tangent of the original angle (A). This formula gives the relationship between the tangent of an angle and its double.

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