यदि ` x=a [cos theta +log tan (theta //2) ]` व ` y= a sin theta, ` तब `theta =(pi//4) ` पर ` (dy)/(dx) ` का मान ज्ञात कीजिए|

Explanation

यहाँ ` " "x =a {cos theta+log tan (theta //2)}`
` 'theta'` के सापेक्ष अवकलन करने पर,
`(dx)/(d theta ) =a{ -sin theta ""+ (sec^(2)(theta//2))/(2tan (theta //2)}}`
` " "= a { -sin theta + ""(1)/(2sin (theta //2) *cos (theta //2)}}`
` =a {-sin theta ""+ (1)/(sintheta )}= (a(1-sin theta ))/(sin theta )=(acos ^(2)theta )/(sin theta )`
अब ` y= asin theta `
` 'x'` के सापेक्ष अवकलन करने पर
` (dy)/(d theta ) =a cos theta `
` rArr " "(dy)/(dx) ={ (duy)/(d theta)xx(d theta )/(dx)}={ a cos theta * ""(sin theta )/(a cos^(2) theta )} =tan theta `
` [(dy)/(dx) ]_(theta =pi //4 )=tan ""(pi)/(4) =1 `