(dy)/(dx)" of "sqrt(sin x+sqrt(sin x+sqrt(sin x)))-oo

Find (dy)/(dx), if y=(sqrt(sin x))/(sin sqrt(x))

If y = sqrt(sin x + sqrt(sin x + sqrt(sin x + ....oo))) then (dy)/(dx)

(d)/(dx) Tan^(-1)[(sqrt(1+sinx) - sqrt(1-sin x))/(sqrt(1+sin x) + sqrt(1-sin x))]=

y= sqrt(sin x + sqrt(sin x + sqrt(sin x + …….oo))) then (dy)/(dx) =………

If y=sqrt(sin x+sqrt(sin x +sqrt(sin x+....oo))) " then prove that " dy/dx = cos x /(2y-1).

Assuming the validity of the operations on the r.h.s. find dy/dt y = sqrt[[sin x + sqrt{{sin x + sqrt((sin x + ........)}])}]

int_(0)^((pi)/(2))(sqrt(sin x))/(sqrt(sin x)+sqrt(cos x))dx

Evaluate int_(0)^(pi//2) (sqrt( sin x))/(sqrt(sin x)+ sqrt(cos x))dx.