求证1/sin^2a+3/cos^2a>=4+2根号下3
1/sin²a +3/cos²a
=(sin²a+cos²a)/sin²a +3(sin²a+cos²a)/cos²a
=1+cos²a/sin²a+3+3sin²a/cos²a
=4+cos²a/sin²a+3sin²a/cos²a
≥4+2√[(cos²a/sin²a)(3sin²a/cos²a)]=4+2√3
人气：346 ℃ 时间：2020-02-06 08:01:14
解答
1 /sin²a +3 /cos²a
=csc²a +3sec²a
=cot²a+1 +3 (tan²a+1)
=4+cot²a+3tan²a≥4 +2√(cot²a*3tan²a)=4 +2√3.
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