if `x = sec theta - cos theta and y = sec^n theta - cos^n theta`, then show that `(x^2+4)(dy/dx)^2 = n^2(y^2+4)`

If y = sec^2 theta+ cos^2 theta, theta ne 0 , then :

If x = a cos theta + b sin theta and y =asin theta-b cos theta , then prove that y^2 (d^2y)/(dx^2)-x(dy)/(dx)+y=0

If x = 2 cos theta - cos 2 theta, y = 2 sin theta - sin 2 theta, find dy/dx at theta = pi/2

If m= sin theta+ cos theta and n= sec theta+cosec theta , prove that n (m + 1) (m-1) = 2m .

If cot theta+cos theta=m, cot theta-cos theta=n , show that : (m^2-n^2)^2=16mn .

Find dy/dx when x = cos theta + cos 2 theta, y = sin theta + sin 2 theta)

Find dy/dx , if x = cos(theta) and y = sin(2theta)

x = a (theta - sin theta), y = a (1 + cos theta) find dy/dx

x = a (theta + sin theta), y = a (1 - cos theta) find dy/dx

If x = a (sin theta - theta cos theta) and y = a (cos theta + theta sin theta) find dy/dx at theta = pi/4