$$tan12Sin$$−$$12x1+x2$$−$$12Cos$$−$$11$$−$$y21+y2=$$

Question

Infinity Learn · Accepted Answer

Let $$x=tanA$$;$$y=tanB$$.  Then $$tan12sin-12x1+x2-12cos-11-x21+x2=tan12sin-12tanA1+tanA2-12cos-11-tanB21+tanB2$$                                                                          $$=tan12sin-1sin2A-12cos-1cos2B$$                                                                          $$=tanA-B$$                                                                          $$=tanA-tanB1+tanAtanB$$                                                                           $$=x-y1+xy$$

$\tan [\frac{1}{2} S i n^{- 1} (\frac{2 x}{1 + x^{2}}) - \frac{1}{2} C o s^{- 1} (\frac{1 - y^{2}}{1 + y^{2}})] =$

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tan12Sin−12x1+x2−12Cos−11−y21+y2=

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$\tan [\frac{1}{2} S i n^{- 1} (\frac{2 x}{1 + x^{2}}) - \frac{1}{2} C o s^{- 1} (\frac{1 - y^{2}}{1 + y^{2}})] =$