`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`

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

1.	`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`
Answer» 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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