If `y = sqrt((1-sin2x)/(1+sin2x))`, prove that `dy/dx + sec^2 (pi/4 -x) = 0,0 le x le pi/4`

y = (cosx + sin x)/(cosx - sin x), prove that dy/dx = sec^2(pi/4 + x)

If y = (sin^-1x)/(sqrt(1-x^2)) , prove that (1-x^2)(dy/dx)- xy = 1

If sin^-1 x = y , then 0 le y le pi

If y= sin (2 sin^-1 x) , prove that: (1 - x^2 ) (d^2y/dx^2) - x(dy/dx) + 4y = 0 .

Prove that : (1-sin2x)/(1+sin2x)= tan^2 (pi/4-x) .

If y = sin^(-1) ((2x)/(1 + x^2)) + sec^(-1) ((1 + x^2)/(1 - x^2)) , prove that (dy)/(dx) = 4/(1 + x^2) , 0 < x < 1

If y = sin(2 cos^(-1)x) , then prove that (1 - x^2)(d^2y)/(dx) -x dy/dx + 4y = 0

Draw the graph of y=sin x and y=cosx, 0 le x le 2pi