Question

what is the reciprocal of tanb in the triangle below? tanc tana tan^{-1}c tan^{-1}a

Explanation:

Step1: Recall the definition of tangent

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). For \(\tan B\), \(\tan B = \frac{AC}{BC}\).

Step2: Find the reciprocal of \(\tan B\)

The reciprocal of \(\tan B\) is \(\frac{BC}{AC}\).

Step3: Calculate \(\tan C\)

For \(\tan C\), \(\tan C=\frac{BC}{AC}\) (since for angle \(C\), the opposite side is \(BC\) and the adjacent side is \(AC\)).

Answer:

\(\tan C\)