{"common":{"save":0,"post_id":"7303","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"7502","mon_id":"1158767","chapter_id":"1159257","post_id":"7303","question":"<p>Gi&aacute; tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c&nbsp;<span class=\"math-tex\">$A=\\tan1^o \\tan2^o \\tan3^o ... \\tan88^o \\tan89^o$<\/span> l&agrave;:<\/p>","options":["<strong>A. <\/strong>0","<strong>B. <\/strong>2","<strong>C. <\/strong>3","<strong>D. <\/strong>1"],"correct":"4","level":"3","hint":"","answer":"<p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>D.&nbsp;<\/strong>1<\/span><\/p><p>V&igrave;&nbsp;<span class=\"math-tex\">$\\tan(90^o-x)=\\cot x$<\/span>&nbsp;v\u1edbi&nbsp;<span class=\"math-tex\">$0^o < x < 90^o$<\/span>&nbsp;n&ecirc;n&nbsp;<span class=\"math-tex\">$\\tan x . \\tan(90^o-x) = \\tan x .\\cot x = 1$<\/span><\/p><p><span class=\"math-tex\">$A=\\tan1^o \\tan2^o \\tan3^o ... \\tan88^o \\tan89^o$<\/span><\/p><p><span class=\"math-tex\">$A=(\\tan1^o \\tan89^o).(\\tan2^o \\tan88^o)...(\\tan44^o\\tan46^o).\\tan45^o$<\/span><\/p><p><span class=\"math-tex\">$A=\\tan45^o=1$<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-04-14 03:28:05","option_type":"txt","len":0},{"id":"7504","mon_id":"1158767","chapter_id":"1159257","post_id":"7303","question":"<p>Bi\u1ebft <span class=\"math-tex\">$\\sin a+\\cos a=\\sqrt{2}$<\/span>. T&iacute;nh gi&aacute; tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c <span class=\"math-tex\">$\\sin^4a+\\cos^4 a$<\/span>.<\/p>","options":["<strong>A. <\/strong><span class=\"math-tex\">$\\dfrac{3}{2}$<\/span>","<strong>B. <\/strong>&ndash;1","<strong>C. <\/strong><span class=\"math-tex\">$\\dfrac{1}{2}$<\/span>","<strong>D. <\/strong>0"],"correct":"3","level":"3","hint":"","answer":"<p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>C.&nbsp;<\/strong><span class=\"math-tex\">$\\dfrac{1}{2}$<\/span><\/span><\/p><p>Ta c&oacute;:&nbsp;<span class=\"math-tex\">$\\sin a+\\cos a=\\sqrt{2}$<\/span>&nbsp;&hArr;&nbsp;<span class=\"math-tex\">$(\\sin a+\\cos a)^2=2$<\/span>&nbsp;&hArr;&nbsp;<span class=\"math-tex\">$\\sin a.\\cos a=\\dfrac{1}{2}$<\/span><\/p><p>Do \u0111&oacute;&nbsp;<span class=\"math-tex\">$\\sin^4a+\\cos^4 a = (\\sin^2a+\\cos^2 a)^2-2.\\sin^2 a.\\cos^2 a=1-2.\\dfrac{1}{4}=\\dfrac{1}{2}$<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-04-14 03:34:39","option_type":"math","len":0},{"id":"7506","mon_id":"1158767","chapter_id":"1159257","post_id":"7303","question":"<p>Gi&aacute; tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c&nbsp;<span class=\"math-tex\">$3(\\sin^4a+\\cos^4 a)-2(\\sin^6a+\\cos^6 a)$<\/span>&nbsp;l&agrave;:<\/p>","options":["<strong>A. <\/strong>1","<strong>B. <\/strong>2","<strong>C. <\/strong>0","<strong>D. <\/strong>&ndash;3"],"correct":"1","level":"3","hint":"","answer":"<p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>A.&nbsp;<\/strong>1<\/span><\/p><p><span class=\"math-tex\">$\\sin^4a+\\cos^4 a=1-2\\sin^2a\\cos^2 a$<\/span><\/p><p><span class=\"math-tex\">$\\sin^6a+\\cos^6 a=1-3\\sin^2a\\cos^2 a$<\/span><\/p><p><span class=\"math-tex\">$3(\\sin^4a+\\cos^4 a)-2(\\sin^6a+\\cos^6 a)$<\/span><\/p><p>=&nbsp;<span class=\"math-tex\">$3(1-2\\sin^2a\\cos^2 a)-2(1-3\\sin^2a\\cos^2 a)$<\/span><\/p><p>= 3&nbsp;&ndash; 2 = 1<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-04-14 03:41:57","option_type":"txt","len":1}]}