If x = a (cos t + t sin t) and y = a (sin t – t cos t), then find the value of at  (CBSE 2014)

Find , when

x = b sin² θ and y = a cos² θ (CBSE 2014,2016)

If prove that

 (CBSE 2014,2017)

If x = a (cos 2t + 2t sin 2t) and y = a (sin 2t – 2t cos 2t), then find . (CBSE 2015)

Let . If f(x) is continuous at
find a and b.  (CBSE 2016)