sinA+sin^2A=1,cos^2A+cos^6A=?

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sinA+sin^2A=1,cos^2A+cos^6A=?sinA+sin^2A=1,cos^2A+cos^6A=?sinA+sin^2A=1,cos^2A+cos^6A=?设sina=tt+t^2=

sinA+sin^2A=1,cos^2A+cos^6A=?
sinA+sin^2A=1,cos^2A+cos^6A=?

sinA+sin^2A=1,cos^2A+cos^6A=?
设sina=t
t+t^2=1
t^2+t-1=0
delta=1+4=5
t1=-1+√5/2
t2=-1-√5/2(舍)
sina=√5-1/2
cos^2A+cos^6A
=sinA+sin^3A
=sinA+sinA(1-sinA)
=sinA+sinA-(sinA)^2
=2sinA-sin^2A
=2sinA-(1-sinA)
=3sinA-1
=3*√5-1/2-1
=3√5-5/2

sinA+sin^2A=1=sin^2A+cos^2A
所以：sinA=cos^2A
cos^2A+cos^6A
=sinA+sin^3A
=sinA+sinA(1-sinA)
=sinA+sinA-(sinA)^2
=2sinA-sin^2A
=2sinA-(1-sinA)
=3sinA-1

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