Question Number 145814 by gsk2684 last updated on 08/Jul/21
$${Let}\:{f}\left({x}\right)=\left\{\mathrm{sin}\:\left(\mathrm{tan}^{−\mathrm{1}} {x}\right)+\mathrm{sin}\:\left(\mathrm{cot}^{−\mathrm{1}} {x}\right)\right\}^{\mathrm{2}} −\mathrm{1} \\ $$$${where}\:\mid{x}\mid>\mathrm{1}\:{and}\:\frac{{dy}}{{dx}}=\frac{\mathrm{1}}{\mathrm{2}}\frac{{d}}{{dx}}\left(\mathrm{sin}^{−\mathrm{1}} {f}\left({x}\right)\right). \\ $$$${if}\:{y}\left(\sqrt{\mathrm{3}}\right)=\frac{\Pi}{\mathrm{6}}\:{then}\:{y}\left(−\sqrt{\mathrm{3}}\right)=? \\ $$