Question

若sinα+ cosα=m,求sin2α-cos4α的值

Answer 1

sinα+cosα=m

(sinα+cosα)^2=m^2

(sinα)^2+(cosα)^2+2sinαcosα=m^2

1+sin2α=m^2

sin2α=m^2-1

sin2α-cos4α

=sin2α-(1-2(sin2α)^2)

=2(sin2α)^2+sin2α-1

=2(m^2-1)^2+(m^2-1)-1

=2m^4-4m^2+2+m^2-1-1

=2m^4-3m^2