Show that :`2tan^(-1)x+sin^(-1)(2x)/(1+x^2)` is constant for `xgeq1,` find that constant.

Explanation

We have `2 tan ^{-1} x+sin ^{-1}(frac{2 x}{1+x^{2}}) for x>1`
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=pi-sin ^{-1}(frac{2 x}{1+x^{2}})+sin ^{-1}(frac{2 x}{1+x^{2}}) because 2 tan ^{-1} x=pi-sin ^{-1}(frac{2 x}{1+x^{2}}), x>1 `
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=pi`
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(For) x=1,2 tan ^{-1} x+sin ^{-1}(frac{2 x}{1+x^{2}}) `
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=2 tan ^{-1} 1+sin ^{-1}(frac{2}{1+1^{2}}) `
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