【已知sina(2cosa-sina)+sin^4a+3cos^4atana=4要讲解】
更新时间： 2025-08-30 08:07:45
5人问答
问题描述：
已知sina(2cosa-sina)+sin^4a+3cos^4atana=4要讲解
戚湧回答：
sina(2cosa-sina)+sin^4a+3cos^4atana
=2sinacosa-sin^2a+sin^4a+3cos^3asina
=2sinacosa+sin^2a(1-sin^2a)+3cos^3asina
=2sinacosa+sin^2acos^2a+3cos^3asina
=sinacosa(2+sinacosa+3cos^2a)
没法化了
戚湧回答：
晕，你的题目抄的有问题，我看错题目了你的题目是tana=4，求sina(2cosa-sina)+sin^4a+3cos^4a对吧？sina(2cosa-sina)+sin^4a+3cos^4a=2sinacosa-sin^2a+sin^4a=2sinacosa+sin^2a(1-sin^2a)=2sinacosa+sin^2acos^2a=2sinacosa+sin^2acos^2a+1-1=(sinacosa+1)^2-1=(sinacosa/1+1)^2-1=[sinacosa/(sin^2a+cos^2a)+1]^2-1=[tana/(1+tan^2a)+1]^2-1=(4/17+1)^2-1=152/289
戚湧回答：
sina(2cosa-sina)+sin^4a+3cos^4a=(2sinacosa-sin^2a)/1+(sin^4a+3cos^4a)/1=(2sinacosa-sin^2a)/(sin^2a+cos^2a)+(sin^4a+3cos^4a)/(sin^2a+cos^2a)=(2tana-tan^2a)/(1+tan^2a)+(sin^2atan^2a+3cos^2a)/(1+tan^2a)=(16sin^2a+3cos^2a)/17=(16sin^2a+3cos^2a)/[17(sin^2a+cos^2a)]=(16tan^2a+3)/[17(tan^2a+1)]=259/289
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