{"common":{"save":0,"post_id":"7302","level":2,"total":10,"point":10,"point_extra":0},"segment":[{"id":"7487","mon_id":"1158767","chapter_id":"1159257","post_id":"7302","question":"<p>Cho bi\u1ebft&nbsp;<span class=\"math-tex\">$\\cos \\alpha = -\\dfrac{2}{3}$<\/span>. T&iacute;nh&nbsp;<span class=\"math-tex\">$\\tan \\alpha$<\/span>.<\/p>","options":["<strong>A. <\/strong><span class=\"math-tex\">$\\dfrac{5}{4}$<\/span>","<strong>B. <\/strong><span class=\"math-tex\">$\\dfrac{\\sqrt{5}}{2}$<\/span>","<strong>C. <\/strong><span class=\"math-tex\">$-\\dfrac{\\sqrt{5}}{2}$<\/span> ","<strong>D. <\/strong><span class=\"math-tex\">$\\dfrac{\\sqrt{5}}{2}$<\/span> ho\u1eb7c <span class=\"math-tex\">$-\\dfrac{\\sqrt{5}}{2}$<\/span>"],"correct":"4","level":"2","hint":"","answer":"<p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>D.&nbsp;<\/strong><span class=\"math-tex\">$\\dfrac{\\sqrt{5}}{2}$<\/span>&nbsp;ho\u1eb7c&nbsp;<span class=\"math-tex\">$-\\dfrac{\\sqrt{5}}{2}$<\/span><\/span><\/p><p>Ta c&oacute;:&nbsp;<span class=\"math-tex\">$1+\\tan ^2\\alpha=\\dfrac{1}{\\cos^2\\alpha}$<\/span><\/p><p>&hArr;&nbsp;<span class=\"math-tex\">$\\tan ^2\\alpha=\\dfrac{1}{\\cos^2\\alpha}-1=\\dfrac{5}{4}$<\/span><\/p><p>&hArr;&nbsp;<span class=\"math-tex\">$\\tan \\alpha=\\dfrac{\\sqrt{5}}{2}$<\/span>&nbsp;ho\u1eb7c&nbsp;<span class=\"math-tex\">$\\tan \\alpha=-\\dfrac{\\sqrt{5}}{2}$<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-04-14 02:07:17","option_type":"math","len":0},{"id":"7489","mon_id":"1158767","chapter_id":"1159257","post_id":"7302","question":"<p>N\u1ebfu&nbsp;<span class=\"math-tex\">$\\cot \\alpha=-\\dfrac{1}{2}$<\/span>&nbsp;th&igrave;&nbsp;<span class=\"math-tex\">$\\cos \\alpha$<\/span>&nbsp;b\u1eb1ng bao nhi&ecirc;u?<\/p>","options":["<strong>A. <\/strong><span class=\"math-tex\">$\\pm \\dfrac{\\sqrt{5}}{5}$<\/span>","<strong>B. <\/strong><span class=\"math-tex\">$\\dfrac{\\sqrt{5}}{2}$<\/span>","<strong>C. <\/strong><span class=\"math-tex\">$- \\dfrac{\\sqrt{5}}{5}$<\/span>","<strong>D. <\/strong><span class=\"math-tex\">$- \\dfrac{1}{3}$<\/span>"],"correct":"1","level":"2","hint":"","answer":"<p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>A.&nbsp;<\/strong><span class=\"math-tex\">$\\pm \\dfrac{\\sqrt{5}}{5}$<\/span><\/span><\/p><p>Ta c&oacute;:&nbsp;<span class=\"math-tex\">$\\cot \\alpha=-\\dfrac{1}{2}$<\/span>&nbsp;&rArr;&nbsp;<span class=\"math-tex\">$\\tan \\alpha=-2$<\/span><\/p><p><span class=\"math-tex\">$1+\\tan^2\\alpha=\\dfrac{1}{\\cos ^2\\alpha}$<\/span>&nbsp;&hArr;&nbsp;<span class=\"math-tex\">$\\cos ^2\\alpha=\\dfrac{1}{1+\\tan^2\\alpha}=\\dfrac{1}{5}$<\/span><\/p><p>&hArr;&nbsp;<span class=\"math-tex\">$\\cos \\alpha= $<\/span>&nbsp;<span class=\"math-tex\">$\\pm \\dfrac{\\sqrt{5}}{5}$<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-04-14 02:13:20","option_type":"math","len":0},{"id":"7490","mon_id":"1158767","chapter_id":"1159257","post_id":"7302","question":"<p>Cho&nbsp;&alpha; l&agrave; g&oacute;c t&ugrave; v&agrave;&nbsp;<span class=\"math-tex\">$\\sin \\alpha=\\dfrac{5}{13}$<\/span>. Gi&aacute; tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c&nbsp;<span class=\"math-tex\">$3\\sin\\alpha+2\\cos\\alpha$<\/span> l&agrave;<\/p>","options":["<strong>A. <\/strong><span class=\"math-tex\">$\\dfrac{9}{13}$<\/span>","<strong>B. <\/strong>3","<strong>C. <\/strong><span class=\"math-tex\">$-\\dfrac{9}{13}$<\/span>","<strong>D. <\/strong>&ndash;3"],"correct":"3","level":"2","hint":"","answer":"<p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>C.&nbsp;<\/strong><span class=\"math-tex\">$-\\dfrac{9}{13}$<\/span><\/span><\/p><p>Ta c&oacute;:&nbsp;<span class=\"math-tex\">$\\cos^2\\alpha=1-\\sin^2\\alpha=\\dfrac{144}{169}$<\/span>&nbsp;&rArr;&nbsp;<span class=\"math-tex\">$\\cos\\alpha=\\pm\\dfrac{12}{13}$<\/span><\/p><p>Do&nbsp;&alpha; l&agrave; g&oacute;c t&ugrave; n&ecirc;n&nbsp;<span class=\"math-tex\">$\\cos\\alpha=-\\dfrac{12}{13}$<\/span><\/p><p>V\u1eady&nbsp;<span class=\"math-tex\">$3\\sin\\alpha+2\\cos\\alpha=3.\\dfrac{5}{13}+2.\\dfrac{-12}{13}=-\\dfrac{9}{13}$<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-04-14 02:20:15","option_type":"math","len":0}]}