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Giải bài 4 trang 65 SGK Toán 10 tập 1 – Chân trời sáng tạo

Cho tam giác ABC. Chứng minh rằng:

꧟Tổng hợp đề thi học kì 2 lớp 10 tất cả các môn - Chân trời sáng tạo

Toán - Văn - Anh - Lí - Hóa - Sinh - Sử - Địa...
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Đề bài

Cho tam giác ABC. Chứng minh rằng: a) \(\sin A = \sin \;(B + C)\) b) \(\cos A =  - \cos \;(B + C)\)

Phương pháp giải - Xem chi tiết

\(\begin{array}{l}\sin \left( {{{180}^o} - A} \right) = \sin A\\\cos \left( {{{180}^o} - A} \right) =  - \cos A\end{array}\)\(({0^o} \le \widehat A \le {180^o})\)

Lời giải chi tiết

Ta có: \(A+B+C=180^o\)a)\(\sin (B + C) = \sin \left( {{{180}^o} - A} \right) = \sin A\)Vậy \(\sin A = \sin \;(B + C)\)b)\(\cos (B + C) = \cos \left( {{{180}^o} - A} \right) =  - \cos A\)Vậy \(\cos A =  - \cos \;(B + C)\)

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