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

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

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

If x cos theta- y sin theta=a,x sin theta+ y cos theta=b , prove that x^2+y^2= a^2+b^2 .

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

If x = a(cos 2theta + 2theta sin 2theta) and y = a(sin 2theta - 2theta cos 2theta) ,find (d^2y/dx^2) at theta = π/8

If x = a (cos theta + theta sin theta) and y = a (sin theta - theta cos theta) , find (d^2y)/(dx^2) at t = pi/4 .

If p and q are the lengths of perpendiculars from the origin to the lines xcos theta -ysin theta = k cos 2 theta and x sec theta + y cosec theta= k , respectively, prove that p^2 + 4q^2 = k^2 .

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