Question

已知sin4次方x-cos4次方x=-五分之四,则sin2x=

Answer 1

sin4次方x-cos4次方x=-五分之四

sin^4x-cos^4x=-4/5

(sin^2x+cos^2x)(sin^2x-cos^2x)=-4/5

1*(sin^2x-cos^2x)=-4/5

sin^2x-cos^2x=-4/5

cos^2x-sin^2x=4/5

cos2x=4/5.余弦二倍角公式

∴sin2x=±3/5