The value of $ an \left\{\frac{1}{2} \sin ^{-1}\left(\frac{2 x}{1+x^2} ight)+\frac{1}{2} \cos ^{-1}\left(\frac{1-y^2}{1+y^2} ight) ight\}$ is

Question

The value of $	an \left\{\frac{1}{2} \sin ^{-1}\left(\frac{2 x}{1+x^2}ight)+\frac{1}{2} \cos ^{-1}\left(\frac{1-y^2}{1+y^2}ight)ight\}$ is

Aicharya · Accepted Answer

Let $x=	an 	heta$ and $y=	an \phi$ $\begin{aligned} & \Rightarrow 	an \left\{\frac{1}{2} \sin ^{-1} \sin 2 	heta+\frac{1}{2} \cos ^{-1} \cos 2 \phiight\} \ & =	an (	heta+\phi) \ & =\frac{	an 	heta+	an \phi}{1-	an 	heta \cdot 	an \phi}=\frac{x+y}{1-x y} \end{aligned}$

The value of $\tan \left\{\frac{1}{2} \sin ^{-1}\left(\frac{2 x}{1+x^2}\right)+\frac{1}{2} \cos…

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