Question

What is the reciprocal of tanB in the triangle below?

Answer 1

Hence, The reciprocal of tan B is tan A

B is correct.

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=\frac{\text{Opposite}}{\text{Base}}`

In ΔABC, ∠C=90°

`\tan B=(AC)/(BC)`

Now we reciprocal it.

`(1)/(\tan B)=(BC)/(AC)`

`\tan A=(BC)/(AC)`

Comparing both equation ( Right sides equal )

`(1)/(\tan B)=(BC)/(AC)=\tan A`

`(1)/(\tan B)=\tan A`

Hence, The reciprocal of tan B is tan A.

Answer 2

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