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int(cos x)/(sqrt(4-sin^(2)x))=?...

`int(cos x)/(sqrt(4-sin^(2)x))=?`

A

`sin^(-1)""(x)/(2)+C`

B

`sin^(-1)""((1)/(2)cosx)+C`

C

`sin^(-1)(2sinx)+C`

D

`sin^(-1)""((1)/(2)sinx)+C`

Text Solution

Verified by Experts

The correct Answer is:
D
Putting sin `x=t` and `cos x dx=dt,` we get
`I=int(dt)/(sqrt(4-t^(2)))=(1)/(2)int (dx)/(sqrt(2^(2)-t^(2)))=sin^(-1)""(t)/(2)+C +sin^(-1)((1)/(2)sinx)+C.`
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