Question

What is the reciprocal of tanB in the triangle below?

Answer 1

Answer:

Hence, The reciprocal of tan B is tan A

B is correct.

Step-by-step explanation:

We are given a right angle triangle. Right angle at ∠C

We need to find the reciprocal of tan B

First we write the formula of tan B using trigonometry identity.

$\tan\theta=\dfrac{\text{Opposite}}{\text{Base}}$

In ΔABC, ∠C=90°

$\tan B=\dfrac{AC}{BC}$

Now we reciprocal it.

$\dfrac{1}{\tan B}=\dfrac{BC}{AC}$

$\tan A=\dfrac{BC}{AC}$

Comparing both equation ( Right sides equal )

$\dfrac{1}{\tan B}=\dfrac{BC}{AC}=\tan A$

$\dfrac{1}{\tan B}=\tan A$

Hence, The reciprocal of tan B is tan A.

Answer 2

Answer:

Step-by-step explanation:

Note that the reciprocal of tan B is by definition the cotangent (cot) of B:

   1                        adjacent side           BC

---------- = cot B = ----------------------- =  ---------

 tan B                   opposite side            AC