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

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

If y = (cosx)^(cosx^(cosx……..to infty)) prove that dy/dx = (-y^2 tanx)/(1-y log cos x)

If sin y = x sin (a + y), then prove that (dy)/(dx) = (sin^(2) (a + y))/(sin a) .

If x cos (a + y)=cos y then prove that [dy/dx = cos^2 (a+ y) /sin a] . Hence show that [sin a (d^2y /dx^2) + sin 2(a+ y) dy/dx =0] .

Prove that (cos^3x - sin^3x)/(cosx - sinx) = (2 + sin2x)/2

int (cos^(2)xsin x)/((sin x- cosx))dx

If y = tan x + sec x , prove that (d^2y)/(dx^2) = (cosx)/((1-sinx)^2)

If x sin (a+y) + sin a cos (a+y) = 0, then prove that : dy/dx = (sin^2(a+y))/(sina)

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 = e^x (sinx + cosx) , prove that (d^2y)/(dx^2)- 2(dy)/(dx) + 2y = 0