sin2a+sina=1 则cos4a+cos2a 2,4代表方
问题描述：
sin2a+sina=1 则cos4a+cos2a 2,4代表方
答
cos^4a+cos^2a
=[(cos^2a)^2+cos^2a
=[1-sin^2a]^2+1-sin^2a
=1-2sin^2a+sin^4a+1-sin^2a
=2-3sin^2a+sin^4a sin^2a=1-sina
=2-3sin^2a+(1-sina)^2
=2-3sin^2a+1-2sina+sin^2a
=3-2sina-2sin^2a
=3-2(sina+sin^2a) sin2a+sina=1
=3-2
=1
答
sin2a+sina=1
1-sin2a=sina
cos4a+cos2a
=(1-sin2a)2+cos2a
=sin2a+cos2a
=1