Question

what is the reciprocal of tan b in the triangle?
a

b c

$\tan^{-1}c$
$\tan c$
$\tan^{-1}a$

Explanation:

Step1: Recall tangent formula

In right - triangle \(ABC\) with right - angle at \(C\), \(\tan B=\frac{AC}{BC}\).

Step2: Find the reciprocal

The reciprocal of \(\tan B\) is \(\frac{BC}{AC}\). And \(\tan C=\frac{BC}{AC}\) (since for angle \(C\), opposite side is \(BC\) and adjacent side is \(AC\)).

Answer:

\(\tan C\)