यदि ` y = sqrt((1-sin 2x)/(1+sin 2x))` तो सिद्ध कीजिए कि
`dy/dx+ sec ^(2) (pi/4-x)=0`

Explanation

`y=sqrt((1-sin2x)/(1+sin 2 x))`
`rArr (sqrt(cos^(2)x+sin^(2)x-2sin x cos x))/(sqrt(cos^(2)x+sin^(2)x+2sin x cos x))`
`=sqrt(((cosx-sinx)/(cosx + sin x))^(2))=(cos x - sin x)/(cos x + sinx )`
`=(1-tanx)/(1+tan x)=(tan (pi)/(4)-tan x)/(1+tan(pi)/(4) tan x)`
`=tan ((pi)/(4)-x)`
`:. (dy)/(dx)=sec^(2)((pi)/(4)-x) (d)/(dx) ((pi)/(4)-x)`
`=sec^(2)((pi)/(4)-x)(-1)`
या `(dy)/(dx)+sec^(2)((pi)/(4)-x)=0` ( इति सिध्दम )