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`int tan^(-1)(cosecx - cotx)dx = ?`

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`int tan^(-1)(cosecx - cotx)dx = ?`
A. `(x^(2))/(4) + C`
B. `(-x^(2))/(4) + C`
C. `(x^(2))/(2) + C`
D. `(-x^(2))/(2) + C`
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1 Answer

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Correct Answer - A
`tan^(-1) (cosec x - cot x) = tan^(-1) (1/(sinx) - (cosx)/(sinx)) = tan^(-1) ((1-cosx)/(sinx))`
`= tan^(-1) {(2sin^(2)(x/2))/(2sin(x/2)cos(x/2))} = tan^(-1) tan(x/2) = x/2`.
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