求证:(1-cosa的4次方-sina的4次方)/(1-cosa的6次方-sina的6次方)=2/311

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/28 00:54:14
求证:(1-cosa的4次方-sina的4次方)/(1-cosa的6次方-sina的6次方)=2/311
x){{fa_|Vɳ5 M۩[}SY*3*[#}cCC"}6h~ =a~O/P}I"T dhE`f`̍IjtCF !D(Q] VO"g TUgix #\tY/i:XpFь)`G8v}Ep5_\gJ Y4P

求证:(1-cosa的4次方-sina的4次方)/(1-cosa的6次方-sina的6次方)=2/311
求证:(1-cosa的4次方-sina的4次方)/(1-cosa的6次方-sina的6次方)=2/3
11

求证:(1-cosa的4次方-sina的4次方)/(1-cosa的6次方-sina的6次方)=2/311
(1-cos^4a-sin^4a)/(1-cos^6a-sin^6a)
=[1-(cos^4a+sin^4a+2cos^2asin^2a)+2cos^2asin^2a]/[1-((cos^2a)^3+(sin^2a)^3)]
=[1-(cos^2a+sin^2a)^2+2cos^2asin^2a]/[1-(cos^2a+sin^2a)(cos^4a+sin^4a-cos^2asin^2a)]
=(2cos^2asin^2a)/[1-(cos^4a+sin^4a-cos^2asin^2a)]
=2cos^2asin^2a/[1-(cos^2a+sin^2a)^2+3cos^2asin^2a]
=2cos^2asin^2a /3cos^2asin^2a
=2/3