यदि ` x=a (cost +log tan ""(t)/(2) ) ` तथा ` y= asin t ` तब `(dy)/(dx) ` का मान ज्ञात कीजिए|

Explanation

` " "x=a (cos t +log tan ""(t)/(2) ) `
` therefore " "(dx)/(dt) =a [(d)/(dt) cos t ""+(d)/(dt) log tan ""(t)/(2)]`
` " "= a [-sin t ""+ (1)/(tan (1//2))sec^(2)""(t)/(2)*(1)/(2)]`
` " "=a [-sin t""+(1)/(2 sin (t//2) cos (t//2))]`
` " "=a [-sin t""+ (1)/(sin t )]=a ((1-sin t)/(sin t ))`
` therefore " "(dx)/(dt) =(acos ^(2)t )/(sin t )" "....(1) `
तथा ` " "y=asin t `
` therefore " "(dy)/(dt) =a cos t " "...(2)`
` because " "(dy)/(dx) =(dy//dt)/(dx//dt) =(acos txxsin t )/(acos ^(2)t ) =tan t `
` therefore " "(dy)/(dx) =tan t `