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int frac{1}{sin(x-a) sin(x-b)} dx =........

`int` `frac{1}{sin(x-a) sin(x-b)}` dx =.......... A) `int` `frac{1}{sin(b-a)}` log`frac{sin(x-b)}{sin(x-a)}` + c B) `int` `frac{1}{sin(a-b)}` log|`frac{sin(x-a)}{sin(x-b)}`| + c C) `int` `frac{1}{cos(a-b)}` log|`frac{sin(x-b)}{sin(x-a)}`| + c D) `int` `frac{1}{cos(a-b)}` log|`frac{sin(x-a)}{sin(x-b)}`| + c

A

(a) `1/(sin(a-b))logabs((sin(x-a))/(sin(x-b)))+c`

B

(b) `-1/(sin(a-b))logabs((sin(x-a))/(sin(x-b)))+c`

C

(c) `logsin(x-a)sin(x-b)+c`

D

(d) `logabs((sin(x-a))/(sin(x-b)))+c`

Text Solution

Verified by Experts

The correct Answer is:
A
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