Question
If $\alpha=2 \tan ^{-1}\left(\frac{1+x}{1-x}\right)$ and $\beta=\sin ^{-1}\left(\frac{1-x^{2}}{1+x^{2}}\right)$ for$0<x<1$, then prove that $\alpha+\beta=\pi$
Step 1
Step 1: We are given that $\alpha=2 \tan ^{-1}\left(\frac{1+x}{1-x}\right)$ and $\beta=\sin ^{-1}\left(\frac{1-x^{2}}{1+x^{2}}\right)$. Show more…
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If $\alpha=2 \tan ^{-1}\left(\frac{1+x}{1-x}\right)$ and $\beta=\sin ^{-1}\left(\frac{1-x^{2}}{1+x^{2}}\right)$ for $0<x<1$, then prove that $\alpha+\beta=\pi$
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