`" If "y=cot^(-1)[(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))](0ltxltpi//2)," then "(dy)/(dx)=`
A. `(1)/(2)`
B. `(2)/(3)`
C. 3
D. 1

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1 Answers

`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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