10分 2題 amaths 請列詳細步驟

1.
LHS = tanx(1-sinx) / (1+cosx)
= sinx(1-sinx)(1-cosx) / cosx(1+cosx)(1-cosx)
= sinx(1-sinx)(1-cosx) / cosx(sinx)^2
= (1-sinx)(1-cosx) / cosxsinx
RHS = cotx(1-cosx)/(1+sinx)
= cosx(1-cosx)(1-sinx) / sinx(1+sinx)(1-sinx)
= cosx(1-cosx)(1-sinx) / sinx(cosx)^2
= (1-cosx)(1-sinx) / sinxcox
= LHS

2.
LHS = (1+cosx+sinx) / (1+cosx-sinx)
= (1+cosx+sinx)^2 / (1+cosx-sinx)(1+cosx+sinx)
= (2+2sinx+2cosx+2sinxcosx) / [2(cosx)^2+2cosx]
= (1+sinx)(2cosx+2) / cosx(2cosx+2)
= (1+sinx) / cosx
= RHS

2006-12-09 00:20:46 補充：
= (1-cosx)(1-sinx) / sinxcoS

2006-12-09 00:21:51 補充：
= (1-cosx)(1-sinx) / sinxcoSx <-- 打少左個s