Question Number 21430 by Tinkutara last updated on 23/Sep/17
$$\mathrm{In}\:\mathrm{any}\:\Delta{ABC},\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{2}{ac}\:\mathrm{sin}\:\left(\frac{{A}\:−\:{B}\:+\:{C}}{\mathrm{2}}\right)\:\mathrm{is} \\ $$
Answered by $@ty@m last updated on 23/Sep/17
$$=\mathrm{2}{ac}\mathrm{sin}\:\left(\frac{\pi−\mathrm{2}{B}}{\mathrm{2}}\right) \\ $$$$=\mathrm{2}{ac}\mathrm{cos}\:{B} \\ $$$$={c}^{\mathrm{2}} +{a}^{\mathrm{2}} −{b}^{\mathrm{2}} \\ $$
Commented by Tinkutara last updated on 23/Sep/17
$$\mathrm{But}\:\mathrm{book}\:\mathrm{says}\:{b}^{\mathrm{2}} −{a}^{\mathrm{2}} −{c}^{\mathrm{2}} .\:\mathrm{I}\:\mathrm{also}\:\mathrm{think} \\ $$$$\mathrm{your}\:\mathrm{answer}\:\mathrm{true}\:\mathrm{because}\:\mathrm{I}\:\mathrm{also}\:\mathrm{got}\:\mathrm{the} \\ $$$$\mathrm{same}\:\mathrm{answer}. \\ $$