Tan^ 11/√(x^2 1) = tan^ 11/√(cosec^2 θ 1) (Putting x = cosec θ ) tan^ 11/cot θ = θ = cosec^ 1 x. ...

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Standard XIII

Mathematics

Composition of Inverse Trigonometric Functions and Trigonometric Functions

tan-11/√x2 - ...

Question

$t a n^{- 1} \frac{1}{\sqrt{x^{2} - 1}} =$

\frac{x}{2} + c o s e c^{- 1} x

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\frac{x}{2} + s e c^{- 1} x

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c o s e c^{- 1} x

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s e c^{- 1} x

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Solution

The correct option is C $c o s e c^{- 1} x$
$t a n^{- 1} \frac{1}{\sqrt{x^{2} - 1}} = t a n^{- 1} \frac{1}{\sqrt{c o s e c^{2} θ - 1}}$
(Putting x = cosec $θ$ )
$t a n^{- 1} \frac{1}{c o t θ} = θ = c o s e c^{- 1} x .$

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tan−11√x2−1=

The correct option is C cosec−1xtan−11√x2−1=tan−11√cosec2 θ−1 (Putting x = cosec θ ) tan−11cot θ=θ=cosec−1 x.

$t a n^{- 1} \frac{1}{\sqrt{x^{2} - 1}} =$

The correct option is C $c o s e c^{- 1} x$
$t a n^{- 1} \frac{1}{\sqrt{x^{2} - 1}} = t a n^{- 1} \frac{1}{\sqrt{c o s e c^{2} θ - 1}}$
(Putting x = cosec $θ$ )
$t a n^{- 1} \frac{1}{c o t θ} = θ = c o s e c^{- 1} x .$