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

If `y=cot^(-1)[(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))]`, `(0 lt x lt pi/2)`, then `(dy)/(dx)=`

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Differentiate w.r.t.x the function in Exercises 1 to 11. cot^(-1)[(sqrt(1+sin x)+sqrt(1-sin x))/(sqrt(1+sin x)-sqrt(1-sin x))],0 lt x lt (pi)/(2) .

Prove that: cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx)))=x/2,x in (0,pi/4)

show that , cot ^(-1) {(sqrt(1+sin x)+sqrt(1- sin x))/( sqrt(1+sin x)- sqrt(1-sin x))}=(x)/(2),0 lt x lt (pi)/(2)

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"if "y=sin^(-1)[sqrt(x)sqrt(1-x^(2))-x sqrt(1-x)] and 0lt x lt 1," then find "(dy)/(dx).

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tan ^(-1) ""{(sqrt(1+cos x)+sqrt(1-cos x)}/{sqrt(1+cosx)-sqrt(1-cos x)}}=(pi)/(4)+(x)/(2) , 0 lt x lt (pi)/(2)

If y="cot"^(-1) (sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)) , show that [(dy)/(dx)]_(x=(1)/(2))= -(1)/(sqrt(3)) .

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