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Let U=sin^(-1)((2x)/(1+x^2)) and V=tan^(...

Let `U=sin^(-1)((2x)/(1+x^2))` and `V=tan^(-1)((2x)/(1-x^2))` , then `(d U)/(d V)=` (a)`1//2` (b) `x` (c) `(1-x^2)/(1+x^2)` (d) 1

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Let `x=tan theta`
`U=sin^(-1)((2tan theta)/(1+tan^2 theta))=sin(-1)(sin^-1(2theta))=2 theta`
`V=tan^(-1)((2tan theta)/(1-tan^2 theta))=tan^(-1)tan 2 theta=2 theta`
`frac{dU}{dV}=frac{frac{dU}{d theta}}{frac{dV}{d theta}}=1`
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