GÕ thử công thức toán học
[TEX] sin Ccos (A-B) = 2.sin A. sin B(1)[/TEX]
[TEX] sin C cos (A-B) = {cos ( A - B ) } + {cos C}[/TEX]
[TEX] sin ^2C cos^2 (A-B) = cos ^2 ( A - B) + cos ^2C + 2 cos ( A - B )cos C[/TEX]
[TEX] 2cos (A-B).cos C + cos^2(A-B)(1-sin^2C) + cos ^2C =0[/TEX]
[TEX] -2cos (A-B).cos C = (cos^2(A-B)+1). cos ^2C [/TEX]
[TEX] \left[ \begin{cos C= 0}\\{(cos^2 (A-B) + 1)cos C =- 2cos (A-B) [/TEX]
TH1: [TEX] cos C =0 [/TEX] ------> [TEX] C =90^o [/TEX]
TH2: [TEX] (cos^2 (A-B) + 1)cos C = -2cos (A-B) [/TEX]
[TEX]\Leftrightarrow (cos(A-B).cosC)^2 + 2 cos(A-B).cos C + 1 = 1- cos ^2 C[/TEX]
[TEX]\Leftrightarrow (cos(A-B) cos C + 1)^2 = sin^2C[/TEX]
[TEX]\Leftrightarrow \mid cos 2A + cos 2B + 1 \mid = sin C[/TEX]
[TEX]\Leftrightarrow cos ^2 A + cos ^2 B = sin C[/TEX]