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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

`ln("sin"(x)/(2))+C`

B

`2ln("cos"(x)/(2))+C`

C

`ln(1-sinx)+C`

D

`In(1-cosx)+C`

Text Solution

Verified by Experts

The correct Answer is:
A
`"f"("cosec "x+cotx-("cosec"^(2)x-cotx))/(1+cotx-"cosec "x)dx=f("cosec "x+cotx)dx` ltbr? `=ln("cosec "x-cotx)+ln sin x+C=ln(1-cosx)+C`
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