If x = a (cos 2t + 2t sin 2t) and y = a (sin 2t – 2t cos 2t), then find .

If x = a (cos t + t sin t) and y = a (sin t – t cos t), then find the value of at

If , y = a sin t, evaluate at

If x = 3 cot t – 2 cos³ t, y = 3 sin t – 2 sin³ t, find .

If x = a sin t – b cos t, y = a cos t + b sin t, prove that .