Looking for a nice solution! :)

\cot^{-1} \frac{y}{\sqrt{1-x^{2}-y^{2}}}=2\tan^{-1} \sqrt{\frac{3}{4x^{2}}-1}-\tan^{-1} \sqrt{\frac{3}{x^{2}}-4} &\\\\ \text{Q. Express the above as a rational integral equation between x and y.}

My attempt went dirty after a few steps. Hope I get a proper solution here. [1]

2 Answers

62
Lokesh Verma ·

try x=sin theta

y = cos theta . sin phi

30
Ashish Kothari ·

Fresh lease of hope. [3] Will surely give it a try! :)

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