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यदि `y= cot ^(-1) sqrt(( 1-sin x)/( 1+sin x ),)` तब `(dy)/(dx) ` का मान ज्ञात कीजिए|

Answer» प्रश्नानुसार `y= cot ^(-1) sqrt((1-sin x ) /( 1+sin x ) ) `
` =cot ^(-1) sqrt ((1+cos ""((pi)/(2) +x))/( 1- cos""((pi )/(2)+x)) )`
` = cot ^(-1) sqrt((2cos ^(2) "((pi) /(4) + (x)/(2)))/( 2sin ^(2) ((pi )/( 4)+ (x)/(2) ) ))`
` " "= cot^(-1) { cot((pi )/(4) +(x)/(2) )} =((pi )/(4)+ (x)/(2) ) `
` y= ((pi)/(4) + (x)/(2)) `
` therefore " "(dy)/(dx) =(d)/(dx) ((pi)/(4) +(x)/(2) ) `
` rArr" "(d)/(dx) ((pi)/(4) )+ (d)/(dx) ((x)/(2))=0 +(1)/(2) =(1)/(2)`


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