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

Answer» माना ` y= tan ^(-1) ""(sqrt ( 1+sin x )+ sqrt (1-sin x ))/(sqrt(1+sin x )- sqrt(1- sin x ) )`
` = tan ^(-1)""( sqrt(1+ sin x + )sqrt ( 1-sin x ) )/( sqrt ( 1+sin x )- sqrt (1-sin x ))xx (sqrt (1+sin x )+ sqrt ( 1-sinx ))/( sqrt(1+sinx )+ sqrt( 1-sin x ))`
` " "= tan ^(-1)"" {( 1+sin x ) + (1-sin x)+ 2sqrt (1-sin ^(2)x ))/((1+sin x )-(1-sin x ))`
` =tan ^(-1)""((1+ cos x ) /( sin x )) =tan ^(-1)""{ (2cos ^(2) (x//2))/(2sin (x//2)cos (x//2))}`
` =tan ^(-1) {cot ""(x)/(2) }=tan ^(-1) {tan ""((pi)/(2)-(x)/(2))} `
` " "y= ((pi)/(2) -(x)/(2))`
` therefore (dy)/(dx) =(d)/(dx) ((pi)/(2)-(x)/(2) ) =(d)/(dx) ((pi)/(2) )-(d)/(dx) ((x)/(2))`
`" "= 0 -(1)/(2) =-(1)/(2) `


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