Prove that: `int_(0)^(pi//2) (sinx)/(sinx +cos x)d dx =(pi)/(4)`

int_(0)^(pi//4)sinx.d(x-[x])=

Differentiate tan^(-1) sqrt((1-cos x)/(1 + cos x)), - (pi)/(4) lt x lt (pi)/(4)

If x in (0,pi/2) then find d/dx(sinx) .

Differentiate w.r.t. x the function (sinx-cosx)^((sinx-cosx)),pi/4 < x < (3pi)/4

Differentiate cos^(-1) ((sin x + cos x)/(sqrt2)), - (pi)/(4) lt x lt (pi)/(4)

Differentiate (sin x - cos x)^(sin x -cos x) , (-pi)/(4) lt x lt (3pi)/4

Differentiate tan^(-1){(cosx)/(1+sinx)},\ 0 le x le pi

The value of the integral int_(-2012pi)^(2012pi) {d/dx(int_0^(x^2) cost^2 dt} dx is

If (d)/(dx)[(sin x)/(sin(x-(pi)/(4)))]=k cos ec^(2)(x-(pi)/(4)) find k and show that it is independent of x .

Differentiate w.r.t. x the function in (sinx-cosx)^((sinx-cosx)),pi/4ltxlt(3pi)/4 .