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Let f(x)=("cosec "x+cotx-1)/(1+cotx-"cos...

Let `f(x)=("cosec "x+cotx-1)/(1+cotx-"cosec "x)`. The Primitive of f(x) with respect to x is equal to

A

`(sinx)/(1-cosx)`

B

`(1-cosx)/(sinx)`

C

`(1+cosx)/(sinx)`

D

`(sinx)/(1+cosx)`

Text Solution

Verified by Experts

The correct Answer is:
C
`(cotx+"cosec "x-("cosec"^(2)x-cot^(2)x))/(cotx-"cosec"x+1)`
`=(cotx+"cosec"x-[("cosec"x-cotx)("cosec"x+cotx)])/(cotx-"cosec"x+1)`
`=((cotx+"cosec"x)(1+cotx-"cosec"x))/((cotx-"cosec"x+1))`
`=cotx+"cosec x"`
`=(cosx)/(sinx)+(1)/(sinx)=(1+cosx)/(sinx)`
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