Question

Simplify the expression cos (tan-1(x/2)).

Answer 1

\cos (\tan \left( -1\right) (\frac{x}{2}))

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Simplify

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Combine multiplied terms into a single fraction

\cos (\tan \left( -1\right) \cdot \frac{x}{2})

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⋅

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\cos (\frac{\tan \left( -1\right) x}{2})

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Solution

\cos \left( \frac{\tan \left( -1\right) x}{2}\right)

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Answer 2

Answer:

Step-by-step explanation:

$cos(tan^{-1}(\frac{x}{2} ))\\put~tan^{-1}(\frac{x}{2} )=t\\\frac{x}{2} =tan~t\\sec^2t-tan^2t=1\\sec^2t=1+tan^2t=1+(\frac{x}{2} )^2=\frac{x^2+4}{4} \\sec~t=\pm\frac{\sqrt{x^2+4}}{2} \\cos ~t=\pm\frac{2}{\sqrt{x^2+4}} \\hence~cos(tan^{-1}(\frac{x}{2} ))=cos~t=\pm\frac{2}{\sqrt{x^2+4}}$