If $x$ is a positive acute angle and $tan x = p$ , $cos x$ is equal to

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

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\sqrt{p^{2} + 1}

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

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\frac{1}{\sqrt{p^{2} - 1}}

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\frac{p}{\sqrt{p^{2} - 1}}

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Solution

The correct option is C $\frac{1}{\sqrt{p^{2} + 1}}$
Given, $tan x = p$
$\Rightarrow sec x = \sqrt{1 + {tan}^{2} x} = \sqrt{1 + p^{2}}$
Therefore $cos x = \frac{1}{sec x} = \frac{1}{\sqrt{1 + p^{2}}}$

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