{"common":{"save":0,"post_id":"7034","level":2,"total":10,"point":10,"point_extra":0},"segment":[{"id":"4695","post_id":"7034","mon_id":"1158924","chapter_id":"1159141","question":"<p>Gi&aacute; tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c<\/p><p><span class=\"math-tex\">$M=sin\\dfrac{\\pi}{24}.sin\\dfrac{5\\pi}{24}.sin\\dfrac{7\\pi}{24}.sin\\dfrac{11\\pi}{24}$<\/span>&nbsp;b\u1eb1ng<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$\\dfrac{1}{2}$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$\\dfrac{1}{4}$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$\\dfrac{1}{8}$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$\\dfrac{1}{16}$<\/span>"],"correct":"4","level":"2","hint":"","answer":"<p>Ta c&oacute;&nbsp;&nbsp;<span class=\"math-tex\">$sin\\dfrac{7\\pi}{24}=cos\\dfrac{5\\pi}{24}$<\/span>&nbsp; v&agrave;&nbsp;&nbsp;<span class=\"math-tex\">$sin\\dfrac{11\\pi}{24}=\\dfrac{\\pi}{24}$<\/span>&nbsp; .<\/p><p>Do \u0111&oacute;&nbsp;&nbsp;<span class=\"math-tex\">$M=sin\\dfrac{\\pi}{24}.sin\\dfrac{5\\pi}{24}.cos\\dfrac{5\\pi}{24}.cos\\dfrac{\\pi}{24}$<\/span>&nbsp;<\/p><p><span class=\"math-tex\">$=\\dfrac{1}{4}.\\bigg(2.sin\\dfrac{\\pi}{24}.cos\\dfrac{\\pi}{24}\\bigg).\\bigg(2.sin\\dfrac{5\\pi}{24}.cos\\dfrac{5\\pi}{24}\\bigg)$<\/span><\/p><p><span class=\"math-tex\">$=\\dfrac{1}{4}.sin\\dfrac{\\pi}{12}.sin\\dfrac{5\\pi}{12}$<\/span><\/p><p><span class=\"math-tex\">$=\\dfrac{1}{4}.\\dfrac{1}{2}\\bigg(cos\\dfrac{\\pi}{3}-cos\\dfrac{\\pi}{2}\\bigg)$<\/span><\/p><p><span class=\"math-tex\">$=\\dfrac{1}{8}.\\bigg(\\dfrac{1}{2}-0\\bigg)=\\dfrac{1}{16}$<\/span><\/p><p>Ch\u1ecdn&nbsp; &nbsp;<span style=\"color:#16a085;\"><strong>D.<\/strong>&nbsp;<span class=\"math-tex\">$\\dfrac{1}{16}$<\/span>&nbsp;.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-11-12 06:21:18","option_type":"math","len":0},{"id":"4696","post_id":"7034","mon_id":"1158924","chapter_id":"1159141","question":"<p>Cho g&oacute;c&nbsp;x&nbsp;th\u1ecfa m&atilde;n&nbsp;<span class=\"math-tex\">$sinx=\\dfrac{3}{5}$<\/span>&nbsp;. T&iacute;nh&nbsp;&nbsp;<span class=\"math-tex\">$P=sin\\bigg(x+\\dfrac{\\pi}{6}\\bigg).sin\\bigg(x-\\dfrac{\\pi}{6}\\bigg)$<\/span>&nbsp;.<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$\\dfrac{11}{100}$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$-\\dfrac{11}{100}$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$\\dfrac{7}{25}$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$\\dfrac{10}{11}$<\/span>"],"correct":"1","level":"2","hint":"","answer":"<p>P =&nbsp;<span class=\"math-tex\">$sin\\bigg(x+\\dfrac{\\pi}{6}\\bigg).sin\\bigg(x-\\dfrac{\\pi}{6}\\bigg)$<\/span>&nbsp;=&nbsp;<span class=\"math-tex\">$\\dfrac{1}{2}\\bigg(cos\\dfrac{\\pi}{3}-cos2x\\bigg)$<\/span>&nbsp;<\/p><p>Ta c&oacute;&nbsp;<span class=\"math-tex\">$cos2x=1-2sin^2x=1-2.\\bigg(\\dfrac{3}{5}\\bigg)^2=\\dfrac{7}{25}$<\/span>&nbsp;.<\/p><p>Do \u0111&oacute;&nbsp; P =&nbsp;<span class=\"math-tex\">$\\dfrac{1}{2}.\\bigg(\\dfrac{1}{2}-\\dfrac{7}{25}\\bigg)=\\dfrac{11}{100}$<\/span>&nbsp;.<\/p><p>Ch\u1ecdn&nbsp; &nbsp;<span style=\"color:#16a085;\"><strong>A.<\/strong>&nbsp;<span class=\"math-tex\">$\\dfrac{11}{100}$<\/span>&nbsp;.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-11-12 06:27:13","option_type":"math","len":0},{"id":"4697","post_id":"7034","mon_id":"1158924","chapter_id":"1159141","question":"<p>Cho g&oacute;c x th\u1ecfa m&atilde;n&nbsp;<span class=\"math-tex\">$cosx=-\\dfrac{4}{5}\u00a0$<\/span>&nbsp; v&agrave;&nbsp;&nbsp;<span class=\"math-tex\">$\\pi < x < \\dfrac{3\\pi}{2}$<\/span>&nbsp;. T&iacute;nh&nbsp; P =&nbsp;<span class=\"math-tex\">$sin\\dfrac{x}{2}.cos\\dfrac{3x}{2}$<\/span>&nbsp;.<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$-\\dfrac{39}{50}$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$\\dfrac{49}{50}$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$-\\dfrac{49}{50}$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$\\dfrac{39}{50}$<\/span>"],"correct":"4","level":"2","hint":"","answer":"<p>P =&nbsp;<span class=\"math-tex\">$sin\\dfrac{x}{2}.cos\\dfrac{3x}{2}$<\/span>&nbsp;=&nbsp;<span class=\"math-tex\">$\\dfrac{1}{2}(sin2x-sinx)$<\/span>&nbsp;=&nbsp;<span class=\"math-tex\">$\\dfrac{1}{2}sinx(2cosx-1)$<\/span>&nbsp;<\/p><p>T\u1eeb h\u1ec7 th\u1ee9c&nbsp;&nbsp;<span class=\"math-tex\">$sin^2x+cos^2x=1$<\/span>&nbsp; v&agrave;&nbsp;&nbsp;<span class=\"math-tex\">$\\pi < x < \\dfrac{3\\pi}{2}$<\/span>&nbsp;, suy ra&nbsp;&nbsp;<span class=\"math-tex\">$sinx=-\\sqrt{1-cos^2x}=-\\dfrac{3}{5}$<\/span>&nbsp;.<\/p><p>Thay&nbsp;<span class=\"math-tex\">$sinx=-\\dfrac{3}{5}$<\/span>&nbsp;v&agrave;&nbsp;<span class=\"math-tex\">$cosx=-\\dfrac{4}{5}$<\/span>&nbsp;v&agrave;o P ta \u0111\u01b0\u1ee3c P =&nbsp;<span class=\"math-tex\">$\\dfrac{39}{50}$<\/span>&nbsp;.<\/p><p>Ch\u1ecdn&nbsp; &nbsp;<span style=\"color:#16a085;\"><strong>D.<\/strong>&nbsp;<span class=\"math-tex\">$\\dfrac{39}{50}$<\/span>&nbsp;.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-11-12 06:35:11","option_type":"math","len":0}]}