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int(sinx)/(sinx-a)dx is equal to...

`int(sinx)/(sinx-a)dx` is equal to

A

`x+sin a cos a log|sin(x-a)|+C`

B

`(cosa)x+sin alog|sin(x-a)|+C`

C

`(sina)x+cosalog|sin(x-a)|+C`

D

None of the above

Text Solution

Verified by Experts

The correct Answer is:
B
`int(sinx)/(sin(x-1))dx=int(sin{(x-a)+a})/(sin(x-1))dx`
`=int(sin(x-a)cosa+cos(x-a)sina)/(sin(x-a))dx`
`=int(sin(x-a)cosa)/(sin(x-a))dx+int(cos(x-a)sina)/(sin(x-a))dx`
`=cosa int 1dx+sin a int cot(x-a)dx`
`=(cosa)x+sina.log|sin(x-a)|+C`
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