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y = cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))...

`y = cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))),find dy/dx.`

A

`(1)/(2)`

B

`(2)/(3)`

C

3

D

1

Text Solution

Verified by Experts

`y=cot^(-1)[(sqrt(1+ sin x)+sqrt(1-sin x))/(sqrt(1+sin x)-sqrt(1-sin x))]`
`=cot^(-1)[(2+2cos x)/(2x)]=cot^(-1)[(1+ cos x)/(sin x)]`
`=cot^(-1)[cos""(x)/(2)]=(x)/(2)`
`therefore" "(dy)/(dx)=(1)/(2)`
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