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Evaluate intsec^(2)x"cosec"^(2)xdx....

Evaluate `intsec^(2)x"cosec"^(2)xdx`.

A

`tanx-cotx+C`

B

`tanx+cotx+C`

C

`-tanx+cotx+C`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
`I=intsec^(2)x(1+cot^(2))dx=intsec^(2)xdx+intsec^(2)xcot^(2)xdx`.
`=tanx+int(1)/(cos^(2)x)*(cos^(2)x)/(sin^(2)x)dx=tanx+int"cosec"^(2)xdx`
`=tanx-cotx+C`.
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