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Evaluate int(1-cosx)"cosec"^(2)xdx...

Evaluate `int(1-cosx)"cosec"^(2)xdx`

Text Solution

Verified by Experts

The correct Answer is:
` "tan"(x)/(2)+C`
`int(1-cosx)"cosec"^(2)xdx=int"cosec"^(2)xdx-int"cosec"xcotxdx`
`=-cotx+"cosec"x+C`
`=(1-cosx)/(sinx)+C`
`=(2"sin"^(2)(x)/(2))/(2"sin"(x)/(2)"cos"(x)/(2))+C`
`"=tan"(x)/(2)+C`
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