作业帮若cos2α=3/5,则sinα^4+cosα^4等于
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/06 14:45:02
若cos2α=3/5,则sinα^4+cosα^4等于
若cos2α=3/5,则sinα^4+cosα^4等于
若cos2α=3/5,则sinα^4+cosα^4等于
cos2α=3/5
2(cosα)^2-1=3/5
2(cosα)^2=8/5
(cosα)^2=4/5
(sinα)^2=1-4/5=1/5
(cosα)^2*(sinα)^2=4/25
sinα^4+cosα^4=［(sinα)^2+(cosα)^2］^2-2(sinα)^2(cosα)^2
=1-2(sinα)^2(cosα)^2
=1-2*4/25
=17/25
第一象限则cos>0 sin 2;α+cos 2;α=1 cosα=3/5 sin2α=2sinα题打的不大明白 sinα^2什么意思还有整体是分式吗？
sinα^4+cosα^4
=sinα^4+cosα^2(1-sinα^2)
=sinα^4+cosα^2-sinα^2cosα^2
=sinα^4-sinα^2cosα^2+cosα^2
=sinα^2(sinα^2-cosα^2)+cosα^2
=-sinα^2(cosα^2-sinα^2)+cosα^2
=-sinα^2*cos2α+cosα^...
全部展开
sinα^4+cosα^4
=sinα^4+cosα^2(1-sinα^2)
=sinα^4+cosα^2-sinα^2cosα^2
=sinα^4-sinα^2cosα^2+cosα^2
=sinα^2(sinα^2-cosα^2)+cosα^2
=-sinα^2(cosα^2-sinα^2)+cosα^2
=-sinα^2*cos2α+cosα^2
=-3sinα^2/5+cosα^2
=-3sinα^2/5+1-sinα^2
=-8sinα^2/5+1
=-8[(1-cos2α)/2]/5+1
=-4(1-cos2α)/5+1
=-4(1-3/5)/5+1
=-(4*2/5)/5+1
=-8/25+1
=17/25
收起