Question

求解一三角题

Answer 1

分子=1-(cos^2 x+sin^2 x)(cos^4 x-cos^2 x*sin^2 x+sin^4 x)
=1-cos^4 x-sin^4 x+cos^2 x*sin^2 x
=3*cos^2 x*sin^2 x （见分母）

分母=cos^2 x+sin^2 x-cos^4 x-sin^4 x=2*cos^2 x*sin^2 x

化简结果为3/2=1.5

Answer 2

(1-cos^6x-sin^6x)/(1-cos^4x-sin^4x)
={1-(cos^2x+sin^2x)(cos^2x-sinxcosx+sin^2x)}/{1-(cos^2x+sin^2x)^2+2sinxcosx}
=(1-1+sinxcosx)/2sinxcosx
=1/2

Answer 3

1－cos^6 x-sin^6 x=1-(cos^2x+sin^2x)(cos^4x-cos^2xsin^2x+sin^4x)=1-cos^4x-cos^4x+cos^2xsin^2x与下式相除＝1+cos^2xsin^2/1-cos^4x-cos^4x＝1+1=2
注：1-cos^4x-cos^4x＝1－(cos^2x+sin^2x)^2+cos^2xsin^2x=cos^2xsin^2x