Chứng minh S_AEF+S_BFD+S_CDE=cos^2A+cos^2B+cos^2C
Cho tam giác ABC nhọn, \(S=1\). Vẽ 3 đường cao AD, BE, CF. C/m:
a) \(S_{AEF}+S_{BFD}+S_{CDE}=cos^2A+cos^2B+cos^2C\)
b)\(S_{DEF}=sin^2A-cos^2B-cos^2C\)
( Gợi ý: a) C/m: \(\dfrac{S_{AEF}}{S_{ABC}}=cos^2A\)