Question

三角函数求证题,在线等.1.tan^2 x-sin^2 x=tan^2 x*sin^2 x2.（1-2sin x*cos

Answer 1

1.(tanx)^2-(sinx)^2=(tanx)^2-(tanxcosx)^2=(tanx)^2*[1-(cosx)^2]=(tanx)^2(sinx)^2

2.(1-2sinxcosx)/[(cosx)^2-(sinx)^2]=(sinx-cosx)^2/[(cosx+sinx)(cosx-sinx)]=(sinx-cosx)/(cosx-sinx)=(tanx-1)/(1-tanx)(同除以cosx)

3.(cosx-1)^2+(sinx)^2=(cosx)^2-2cosx+1+(sinx)^2=2-2cosx

因为：(sinx)^2+(cosx)^2=1

4.(sinx)^4+(cosx)^4=(sinx)^4+2(sinxcosx)^2+(cosx)^4-3(sinxcosx)^2=[(sinx)^2+(cosx)^2]^2-2(sinxcosx)^2=1-2(sinxcosx)^2