यदि ` y= tan ^(-1) ""(cos x)/(1+sin x ),` तो `(dy)/(dx) ` का मान ज्ञात कीजिए|

Explanation

हम जानते है की ` cos x =sin ((pi)/(2)-x)`
तथा ` " "sin x =cos ""((pi)/(2)-x)`
` therefore " "y=tan ^(-1)"" (cos x )/(1+sin x )=tan ^(-1)"" (sin ""((pi)/(2)-x))/(1+cos ((pi )/(2)-x))`
` " "= tan ^(-1) ""(2sin ((pi)/(4) -(x)/(2) )cos ((pi)/(4)-(x)/(2)))/(2cos ^(2) ((pi)/(4)-(x)/(2)))`
`" "= tan ^(-1) [tan ((pi)/4-(x)/(2) )] =(pi)/(4)-(x)/(2) `
` therefore " "(dy)/(dx) =(d)/(dx) ((pi)/(4)-(x)/(2))=(d)/(dx) ((pi)/(4))-(d)/(dx) ((x)/(2))=-(1)/(2)`