Nếu tam giác ABC có \(\frac{{\sin B}}{{\sin C}} = 2\cos A\) thì...?
Tam giác ABC vuông tại A
Tam giác ABC cân tại A
Tam giác ABC cân tại B
Tam giác ABC cân tại C
Hãy suy nghĩ và trả lời câu hỏi trước khi xem đáp án
Ta có: \(\frac{{\sin B}}{{\sin C}} = 2\cos A \Leftrightarrow \sin B = 2\cos A\sin C\)
Mà \(\sin B = \sin ({180^ \circ } - B) = \sin (A + C) = \sin A\cos C + \sin C\cos A\)
\(\begin{array}{l} \Rightarrow \sin A\cos C + \sin C\cos A = 2\cos A\sin C\\ \Leftrightarrow \sin A\cos C = \cos A\sin C\;(*)\end{array}\)
+ Nếu \(\widehat A = {90^ \circ } \Leftrightarrow \cos A = 0 \Leftrightarrow \sin {90^ \circ }.\cos C = 0 \Leftrightarrow \widehat C = {90^ \circ }\) (Vô lí)
+ Nếu \(\widehat A,\widehat C \ne {90^ \circ }\) thì \((*) \Leftrightarrow \frac{{\sin A}}{{\cos A}} = \frac{{\sin C}}{{\cos C}}\) hay \(\tan A = \tan C\)
Suy ra \(\widehat A = \widehat C\) do \({0^ \circ } < \widehat A,\widehat C < {180^ \circ }\)
Vậy tam giác ABC cân tại B.
Chọn C.
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Tính tỉ số
Hình ảnh nào không xuất hiện trong sáu câu thơ đầu của bài thơ Thu điếu?