Find dy/dx, when If x = a sin 2t (1 + cos 2t) and y = b cos 2t (1 – cos 2t), show that at t = π/4, dy/dx = b/a.

Question

Find \(\cfrac{dy}{d\mathrm x} \), when

If x = a sin 2t (1 + cos 2t) and y = b cos 2t (1 – cos 2t), show that at t = \(\cfrac{\pi}4\), \(\cfrac{dy}{d\mathrm x} \) = \(\cfrac{b}a\).

Answer 1

considering the given functions,

x = a sin 2t(1 + cos 2t) and y = b cos 2t(1- cos 2t)

rewriting the above equations,

x = a sin 2t sin 4t

differentiating above function with respect to t, we have,

differentiating above function with respect to t, we have,

from equation 1 and 2