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HomeLớp 11Toán lớp 11 - Sách kết nối tri thứcBài 1. Giá trị lượng giác của góc lượng giác.Bài tập nâng cao
{"common":{"save":0,"post_id":"7032","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"4712","post_id":"7032","mon_id":"1158924","chapter_id":"1159141","question":"<p>Cho cosα = <span class=\"math-tex\">$\\dfrac{2}{3}$<\/span>. Tính A = <span class=\"math-tex\">$\\dfrac{tan\\alpha+3cot\\alpha}{tan\\alpha+cot\\alpha}$<\/span>.<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$\\dfrac{-5}{3}$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$\\dfrac{27}{5}$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$\\dfrac{17}{9}$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$\\dfrac{-9}{2}$<\/span>"],"correct":"3","level":"3","hint":"","answer":"<p>Ta có: <span class=\"math-tex\">$\\dfrac{tan\\alpha+3cot\\alpha}{tan\\alpha+cot\\alpha}$<\/span><\/p><p>= <span class=\"math-tex\">$\\dfrac{tan\\alpha+\\dfrac{3}{tan\\alpha}}{tan\\alpha+\\dfrac{1}{cot\\alpha}}$<\/span> = <span class=\"math-tex\">$\\dfrac{tan^2\\alpha+3}{tan^2\\alpha+1}$<\/span> = <span class=\"math-tex\">$\\dfrac{\\dfrac{1}{cos^2\\alpha}+2}{\\dfrac{1}{cos^2\\alpha}}$<\/span><\/p><p>= <span class=\"math-tex\">$1+2cos^2\\alpha$<\/span><\/p><p>= <span class=\"math-tex\">$1+2.\\dfrac{4}{9}=\\dfrac{17}{9}$<\/span><\/p><p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>C.<\/strong> <span class=\"math-tex\">$\\dfrac{17}{9}$<\/span><\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-11-16 01:28:48","option_type":"math","len":0},{"id":"4714","post_id":"7032","mon_id":"1158924","chapter_id":"1159141","question":"<p>Cho cotα = <span class=\"math-tex\">$\\sqrt{5}$<\/span>. Tính C = <span class=\"math-tex\">$sin^2\\alpha-sin\\alpha cos\\alpha +cos^2\\alpha$<\/span>.<\/p>","options":["<strong>A. <\/strong><span class=\"math-tex\">$\\dfrac{1-\\sqrt{5}}{3}$<\/span>","<strong>B. <\/strong><span class=\"math-tex\">$\\dfrac{6-\\sqrt{5}}{6}$<\/span>","<strong>C. <\/strong><span class=\"math-tex\">$\\dfrac{\\sqrt{5}}{2}$<\/span>","<strong>D. <\/strong><span class=\"math-tex\">$\\dfrac{-6+\\sqrt{5}}{6}$<\/span>"],"correct":"2","level":"3","hint":"","answer":"<p>Ta có: C = <span class=\"math-tex\">$sin^2\\alpha-sin\\alpha cos\\alpha +cos^2\\alpha$<\/span><\/p><p>= <span class=\"math-tex\">$sin^2\\alpha\\space . \\space\\dfrac{sin^2\\alpha-sin\\alpha cos\\alpha +cos^2\\alpha}{sin^2\\alpha}$<\/span><\/p><p>= <span class=\"math-tex\">$sin^2\\alpha\\space . \\space \\bigg(1-\\dfrac{cos\\alpha}{sin\\alpha}+\\dfrac{cos^2\\alpha}{sin^2\\alpha}\\bigg)$<\/span><\/p><p>= <span class=\"math-tex\">$\\dfrac{1}{1+cot^2\\alpha}\u200b\u200b\\space . (1-cot\\alpha+cot^2\\alpha)$<\/span><\/p><p>= <span class=\"math-tex\">$\\dfrac{1}{1+5}\u200b\u200b\\space . (1-\\sqrt{5}+5)$<\/span><\/p><p>= <span class=\"math-tex\">$\\dfrac{6-\\sqrt{5}}{6}$<\/span><\/p><p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>B. <\/strong><span class=\"math-tex\">$\\dfrac{6-\\sqrt{5}}{6}$<\/span><\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-11-16 01:37:13","option_type":"math","len":0},{"id":"4715","post_id":"7032","mon_id":"1158924","chapter_id":"1159141","question":"<p>Rút g\u1ecdn các bi\u1ec3u th\u1ee9c A = sin²α cos²α + sin²α + cos<span class=\"math-tex\">$^4$<\/span>α ta \u0111\u01b0\u1ee3c<\/p>","options":["<strong>A.<\/strong> 1","<strong>B.<\/strong> sin²α","<strong>C.<\/strong> cos²α","<strong>D.<\/strong> 2"],"correct":"1","level":"3","hint":"","answer":"<p>Ta có: A = sin²α cos²α + sin²α + cos<span class=\"math-tex\">$^4$<\/span>α<\/p><p>= sin²α + cos²α . (sin²α + cos²α)<\/p><p>= sin²α + cos²α . 1<\/p><p>= sin²α + cos²α<\/p><p>= 1<\/p><p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>A.<\/strong> 1<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-11-16 01:40:30","option_type":"txt","len":2}]}