If`y=sin[2tan^(-1){sqrt((1-x)/(1+x))}],`find`(dy)/(dx)`

1.	If`y=sin[2tan^(-1){sqrt((1-x)/(1+x))}],`find`(dy)/(dx)`
Answer» `y=sin[2tan^-1 (sqrt(1-x)/(1+x))]` `x=Costheta` `y=sin[2tan^-1 (sqrt(1-Costheta)/(1+Costheta))]` `y=sin[2tan^-1 (sqrt(2-Sin^2theta/2)/(1+Cos^2theta/2))]` `y= sin[2tan^-1tan(theta/2)]` `y=Sintheta` `x=Costheta` `(dy)/(d theta)=costheta=x` `(dx)/(d theta)=-sintheta=-y` `(dy)/(dx)=(dy)/(d theta).(d theta)/(dx)=(x)(-1)/(y)` `(dy)/(dx)=-x/y`

Discussion

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