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

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

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

lim_(xto0)(sqrt(1+sinx)-sqrt(1-sinx))/tanx

Find int(cosx)/(sqrt(1+sinx))dx

y = tan^(-1)((sqrt(x)+sqrt(a))/(1-sqrt(ax))), find dy/dx.

y=e^(sinx^(2)), find dy/dx :

int (cosx)/(sqrt(2+sinx))dx

The number of integers in the range of the function f(x)=|4((sqrt(cosx)-sqrt(sinx))(sqrt(cosx)+sqrt(sinx)))/((cosx+sinx))| is ________.

The number of integers in the range of the function f(x)=|4((sqrt(cos"x")-sqrt(sinx))(sqrt(cos"x")+sqrt(sinx)))/(cosx+sinx)| is______