Which formula is used to find tan(x) if tan(x/2) is known?

The correct choice for finding tan(x) given tan(x/2) is based on the tangent double angle identity. The formula that relates tan(x) to tan(x/2) is derived from trigonometric identities and is crucial in converting half-angle tangent values into full-angle tangent values.

When we have tan(x/2), the relationship can specifically be expressed as:

[ \tan(x) = \frac{2 \tan(x/2)}{1 - \tan^2(x/2)} ]

This formula effectively utilizes the tangent of half an angle to derive the tangent of the full angle. In this context, tan(x/2) serves as the input representing half of the angle x. Applying this identity will allow us to calculate tan(x) accurately.

Understanding this formula is important for transforming half-angle values to full-angle values in trigonometry. It combines the value of the tangent at half the angle to express the tangent at the full angle, ensuring that the identity holds true within the constraints of the tangent function.