If x = ( 2 cos theta – cos 2 theta ) and y = ( 2 sin theta – sin 2 theta ), find ( d2y/dx2)theta= pai/2 The answer: -3/2 Share with your friends Share 6 Varun.Rawat answered this We have, x = 2 cos θ - cos 2θ⇒dxdθ = - 2 sin θ + 2 sin 2θWe have, y = 2 sin θ - sin 2θ⇒dydθ = 2 cos θ - 2 cos 2θNow, dydx = dydθ×dθdx = 2 cos θ - 2 cos 2θ2 sin 2θ - 2 sin θ⇒dydx = cos θ - cos 2θsin 2θ - sin θ⇒dydx = 2 sin θ2 . sin 3θ22 cos 3θ2 . sinθ2 = tan3θ2Now, d2ydx2 = 32sec23θ2 × dθdx⇒d2ydx2 =32sec23θ2 ×12 sin 2θ - 2 sin θ⇒d2ydx2θ=π2=32 sec23π4 × 12 sin π - 2 sin π/2⇒d2ydx2θ=π2 = 32 × -22 × 10 - 2 = -32 16 View Full Answer