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Evaluate `int(1-cosx)"cosec"^(2)xdx`A. `tanx+C`B. `tan.(x)/(2)+C`C. `(1)/(2)tan.(x)/(2)+C`D. None of these

Answer» Correct Answer - B
`int(1-cosx)"cosec"^(2)xdx`
`=int"cosec"^(2)xdx-int"cosec"^(2)xcosxdx`
`=-cotx+"cosec x"+C=(1-cosx)/(sinx)+C`
`=(2sin^(2).(x)/(2))/(2sin.(x)/(2)cos.(x)/(2))+C`
`=tan.(x)/(2)+C`


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