If `x=sin t-t cos t and y = t sin t +cos t,` then what is `(dy)/(dx)` at point `t=(pi)/(2)?`

If `x=sin t-t cos t and y = t sin t +cos t,` then what is `(dy)/(dx)`

1.	If `x=sin t-t cos t and y = t sin t +cos t,` then what is `(dy)/(dx)` at point `t=(pi)/(2)?`
Answer» Correct Answer - A As given: `x=sint-t cos t and y=t sin t+cost` On differentiating w.r.t. t, we get `(dx)/(dt)=cost-{cost+t(-sint)}` `rArr(dx)/(dt)=cost-cost+t sin t=t sint` and, `(dy)/(dt)=t cost+sint-sint=t cost` Hence, `(dy)/(dx)=(dy//dt)/(dx//dt)=(t cos t)/(t sin t)=cot t` `rArr((dy)/(dx))_(t=(pi)/(2))=cot.(pi)/(2)=0`