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Bài 6 trang 24 SGK Toán 11 tập 1 - Chân trời sáng tạo

Chứng minh rằng tam giác ABC, ta có (sin A = sin B.cos C + sin C.cos B)

🔥Tổng hợp đề thi học kì 2 lớp 11 tất cả các môn - Chân trời sáng tạo

Toán - Văn - Anh - Lí - Hóa - Sinh
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Đề bài

Chứng minh rằng tam giác ABC, ta có \(\sin A = \sin B.\cos C + \sin C.\cos B\)

Phương pháp giải - Xem chi tiết

Sử dụng định lý tổng 3 góc trong một tam giác bằng 1800 và áp dụng công thức cộng.

Lời giải chi tiết

Ta có: \(A + B + C = {180^0}\) (tổng 3 góc trong một tam giác) \(\begin{array}{l} \Rightarrow A = {180^0} - \left( {B + C} \right)\\ \Leftrightarrow \sin A = \sin \left( {{{180}^0} - \left( {B + C} \right)} \right)\\ \Leftrightarrow \sin A = \sin \left( {B + C} \right) = \sin B.\cos C + \sin C.\cos B\end{array}\)

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