Problem 84 - Algebra and Trigonometry

Question

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

Step-by-Step Solution

Answer

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 1 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:\[\tan(2A) = \frac{{2\tan(A)}}{{1 - \tan^2(A)}}\]

Step 2 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.