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If x > 0, then \cos (\tan ^{-1}x), in terms of x is 

Option: 1

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


Option: 2

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


Option: 3

\\ {1+x^{2}}


Option: 4

{\text { None of these }}


Answers (1)

best_answer

Let tan-1 x = Θ,

So, tan Θ = x

We have the following right angled triangle

From the figure

\\ \cos \theta= \frac{1}{\sqrt{1+x^2}}\\ \cos (\tan ^{-1}x)=\cos \theta= \frac{1}{\sqrt{1+x^2}}

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