COMPLETE Solving the identity, \( \tan (A)= \) \( \pm \frac{7}{9} \) \( \pm \frac{\sqrt{7}}{9} \)

The solution to the identity involves using the definitions of tangent and the Pythagorean theorem. The tangent function represents the ratio of the opposite side to the adjacent side in a right triangle. If \( \tan(A) = \pm \frac{7}{9} \), we can think of this in terms of a triangle where the opposite side is 7 units and the adjacent side is 9 units. Furthermore, the relationship provided allows us to derive the hypotenuse using the Pythagorean theorem, which states that \( c^2 = a^2 + b^2 \). In this case, the hypotenuse would be \(\sqrt{7^2 + 9^2} = \sqrt{49 + 81} = \sqrt{130}\). This means you can compute \(\sin(A) = \frac{7}{\sqrt{130}}\) and \(\cos(A) = \frac{9}{\sqrt{130}}\) if needed, showcasing how these identities interrelate in trigonometric functions!