Question

Cho tam giác ABC vuông ở A. CMR: \(\frac{AB}{AC}=\frac{\cos B}{\cos C}\)

Answer 1

Tam giác ABC vuông ở A, ta có:

     \(\cos B=\frac{AB}{BC}\);     \(\cos C=\frac{AC}{BC}\).

Vậy \(\frac{\cos B}{\cos C}=\frac{AB}{BC}:\frac{AC}{BC}=\frac{AB}{BC}.\frac{BC}{AC}=\frac{AB}{AC}\).

Answer 2

Ta có: \(\cos B=\frac{AB}{AC}\)

\(\cos C=\frac{AC}{BC}\)

\(\Rightarrow\frac{\cos B}{\cos C}=\frac{\frac{AB}{BC}}{\frac{AC}{BC}}=\frac{AB}{BC}.\frac{BC}{AC}=\frac{AC}{BC}\left(đpcm\right)\)

\(\Rightarrow\frac{AB}{AC}=\frac{\cos B}{\cos C}\)