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`intcos^(-1)((1-tan^(2)x)/(1+tan^(2)x)) dx = ?`

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`intcos^(-1)((1-tan^(2)x)/(1+tan^(2)x)) dx = ?`
A. `x^(2) + C`
B. `-x^(2) + C`
C. `1/(sqrt(1+x^(2))) + C`
D. `1/(sqrt(1-x^(2))) + C`
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1 Answer

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Correct Answer - A
`cos^(-1)((1-tan^(2)x)/(1+ tanx^(2)x)) = cos^(-1) ((cos^(2)x - sin^(2)x)/(cos^(2)x + sin^(2)x))`
`= cos^(-1) (cos^(2)x - sin^(2)x) = cos^(-1) (cosx) = 2x`.
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