Question

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

Answer 1

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