Question

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

Answer 1

Explanation:

`cos(tan^(-1)((x)/(2) ))\\put~tan^(-1)((x)/(2) )=t\\(x)/(2) =tan~t\\sec^2t-tan^2t=1\\sec^2t=1+tan^2t=1+((x)/(2) )^2=(x^2+4)/(4) \\sec~t=\pm(√(x^2+4))/(2) \\cos ~t=\pm(2)/(√(x^2+4)) \\hence~cos(tan^(-1)((x)/(2) ))=cos~t=\pm(2)/(√(x^2+4))`

Answer 2

\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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