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Bài 1.15 trang 19 SGK Toán 11 tập 1 - Cùng khám phá

Cho góc (alpha ) như trong Hình 1.30. Tính (tan alpha ).
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Đề bài

Cho góc \(\alpha \) như trong Hình 1.30. Tính \(\tan \alpha \).

Phương pháp giải - Xem chi tiết

Áp dụng công thức cộng. \(\tan \left( {a - b} \right) = \frac{{\tan a - \tan b}}{{1 + \tan a\tan b}}\)

Lời giải chi tiết

Gọi điểm K như trên hình\(\begin{array}{l}\tan \widehat {CAB} = \frac{{BC}}{{AB}} = \frac{{CK + BK}}{{AB}} = \frac{8}{{10}}\\\tan \widehat {KAB} = \frac{{BK}}{{AB}} = \frac{3}{{10}}\\\tan \alpha  = \tan \left( {\widehat {CAB} - \widehat {KAB}} \right) = \frac{{\tan \widehat {CAB} - \tan \widehat {KAB}}}{{1 + \tan \widehat {CAB}\tan \widehat {KAB}}} = \frac{{25}}{{62}}\end{array}\)

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