{"common":{"save":0,"post_id":"6322","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"5836","mon_id":"1158767","chapter_id":"1158829","post_id":"6322","question":"<p>Bi\u1ebft <span class=\"math-tex\">$\\sin\\alpha+\\cos\\alpha=\\sqrt{2}$<\/span>&nbsp;. H\u1ecfi gi&aacute; tr\u1ecb c\u1ee7a <span class=\"math-tex\">$\\sin^4\\alpha+\\cos^4\\alpha$<\/span>&nbsp; b\u1eb1ng bao nhi&ecirc;u?<\/p>","options":["A. <span class=\"math-tex\">$\\frac{3}{2}$<\/span> . ","B. <span class=\"math-tex\">$\\frac{1}{2}$<\/span> . ","C. -1.","D. 0 ."],"correct":"2","level":"3","hint":"","answer":"<p><span style=\"color:#27ae60;\"><strong>Ch\u1ecdn&nbsp;&nbsp; &nbsp;B.<\/strong><\/span><br \/>Ta c&oacute;: &nbsp;<span class=\"math-tex\">$\\sin\\alpha+\\cos\\alpha=\\sqrt{2}\\Rightarrow(\\sin\\alpha+\\cos\\alpha)^2\\Rightarrow \\sin\\alpha.\\cos\\alpha=\\frac{1}{2}$<\/span> &nbsp;.<br \/><span class=\"math-tex\">$\\sin^4\\alpha+\\cos^4\\alpha=(\\sin^2\\alpha+\\cos^2\\alpha)-2\\sin^2\\alpha.\\cos^2\\alpha=1-2(\\frac{1}{2})^2=\\frac{1}{2}$<\/span>&nbsp;.<\/p>","type":"choose","extra_type":"classic","user_id":"147","test":"0","date":"2022-10-19 06:39:36","option_type":"math","len":0},{"id":"5837","mon_id":"1158767","chapter_id":"1158829","post_id":"6322","question":"<p>Bi\u1ec3u th\u1ee9c: <span class=\"math-tex\">$f(x)=\\cos^4x+\\cos^2x.\\sin^2x+\\sin^2x$<\/span>&nbsp; c&oacute; gi&aacute; tr\u1ecb b\u1eb1ng<\/p>","options":["A. 1 .","B. 2 . ","C. -2 .","D. -1 ."],"correct":"1","level":"3","hint":"","answer":"<p><span style=\"color:#27ae60;\"><strong>Ch\u1ecdn&nbsp;&nbsp; &nbsp;A.<\/strong><\/span><br \/><span class=\"math-tex\">$f(x)=\\cos^2x(\\cos^2x+\\sin^2x)+\\sin^2x=\\cos^2x+\\sin^2x=1$<\/span>&nbsp;.<\/p>","type":"choose","extra_type":"classic","user_id":"147","test":"0","date":"2022-10-19 06:46:17","option_type":"txt","len":0},{"id":"5838","mon_id":"1158767","chapter_id":"1158829","post_id":"6322","question":"<p>Gi&aacute; tr\u1ecb c\u1ee7a <span class=\"math-tex\">$B=\\cos^273^o+\\cos^287^o+\\cos^23^o+\\cos^217^o$<\/span>&nbsp; l&agrave;<\/p>","options":["A. <span class=\"math-tex\">$\\sqrt{2}$<\/span> .","B. 2.","C. -2.","D. 1 ."],"correct":"2","level":"3","hint":"","answer":"<p><span style=\"color:#27ae60;\"><strong>Ch\u1ecdn&nbsp;&nbsp; &nbsp;B.<\/strong><\/span><br \/>&nbsp;<span class=\"math-tex\">$B=(\\cos^273^o+\\cos^217^o)+(\\cos^287^o+\\cos^23^o)\\\\=(\\cos^273^o+\\sin^273^o)+(\\cos^287^o+\\sin^287^o)=2$<\/span>.<\/p>","type":"choose","extra_type":"classic","user_id":"147","test":"0","date":"2022-10-19 06:51:55","option_type":"math","len":0}]}