Q49 of 96 Page 12

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

Formula: –

Given: –

x = asint – bcost,y = accost + bsint

differentiating both w.r.t t

Dividing both

Differentiating w.r.t t

Putting the value

Dividing them

Hence proved.

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

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

Find A and B so that y = A sin 3x + Bcos 3x satisfies the equation

If y = A e ^{– kt} cos (pt + c), prove that , where n² = p² + k².