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int(dx)/(sqrt(sin^3xsin(x+alpha)))...

`int(dx)/(sqrt(sin^3xsin(x+alpha)))`

A

`2" cosec"alpha sqrt(cos alpha+sin alpha.cot x)+C`

B

`-2 "cosec "alpha sqrt(cos alpha+sin alpha .cot x)+C`

C

`"cosec "alpha sqrt(cos alpha +sin alpha +sin alpha . Cotx)+C`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
`int(dx)/(sqrt(sin^(3)x.sin(x+alpha)))`
`=int(dx)/(sqrt(sin^(3)x(sinx.cosalpha+cosx.sinalpha)))`
`=int("cosec"^(2)xdx)/(sqrt(cos alpha+sin alpha.cot x))`
`"Let "t=cos alpha+sin alpha.cot x`
`rArr" "dt=-sin alpha "cosec"^(2)xdx`
`therefore" "(-1)/(sin alpha)int(dt)/(sqrtt)=-"2 cosec" alpha.sqrt(cos alpha+sin alpha.cot x)+C`
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