MathematicsThe value of the trigonometric function tan (cot-1x) is equal to?

The value of the trigonometric function tan ( $\cot^{- 1} x$ ) is equal to?

A
$\frac{1}{x}$
B
cot ( $\tan^{- 1} x$ )
C
Both
D
None

Solution:

We know that (

\cot^{- 1} x

) =

\tan^{- 1} \frac{1}{x}

; x > 0
Given, tan (

\cot^{- 1} x

)

\Rightarrow

tan (

\tan^{- 1} \frac{1}{x}

)
Now using the property tan (

\tan^{- 1} x

) = x, x

\in

R we get,

\Rightarrow

\frac{1}{x}

.
Also, tan (

\cot^{- 1} x

)

\Rightarrow

tan

(\frac{Π}{2} - \tan^{- 1} x)

By using Cot

Θ

= tan

(\frac{Π}{2} - Θ)

we get

\Rightarrow

cot

{(\tan}^{- 1} x)

.

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