Tan ( sec^ 1√(1+x^2) ) = tan ( sec^ 1√(1+tan^2 θ) ) (Putting x = tan θ) = tan(sec^ 1 sec θ) = tan θ = x. ...

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Composition of Trigonometric Functions and Inverse Trigonometric Functions

tan [ sec-1√1...

Question

$t a n [s e c^{- 1} \sqrt{1 + x^{2}}] =$

$\frac{1}{x}$

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\frac{1}{\sqrt{1 + x^{2}}}

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$\frac{x}{\sqrt{1 + x^{2}}}$

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Solution

The correct option is B
x

$t a n (s e c^{- 1} \sqrt{1 + x^{2}}) = t a n (s e c^{- 1} \sqrt{1 + t a n^{2} θ})$
(Putting $x = t a n θ$ )
$= t a n (s e c^{- 1} s e c θ) = t a n θ = x$ .

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