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 + sinx) + sqrt(1 - sinx))/(sqrt(1 + sinx) - sqrt(1 - sinx))]= x/2

(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))=? (x is in IV quadrant)

Write the simplest form : cot^(-1) [(sqrt(1+sinx)+sqrt(1-sin x))/(sqrt(1+sinx)-sqrt(1-sin x)]], x epsilon [0, pi/4]

If y(x) = cot^(-1) ((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))), x in ((pi)/(2), pi) , then (dy)/(dx) at x=(5pi)/(6) is :

If y="tan"^(-1)((sqrt(1+sinx)+sqrt(1-sinx)))/((sqrt(1+sinx)-sqrt(1-sinx)))," find "(dy)/(dx).

value of int_0^1cot^-1((sqrt(1+sinx)+(sqrt(1-sinx)))/((sqrt(1+sinx)-(sqrt(1-sinx)))))dx

If coty=(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))," then "(dy)/(dx)=

Differentiate w.r.t. x the function in cot^(-1)[(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))],0ltxltpi/2

Find (dy)/(dx) of y=cot^(-1)[(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))]