證明下列等式(1+1/cosx+tanx)/(1+1/cosx-tanx)=(1+sinx)/cosx

數(shù)學(xué)人氣：206 ℃時(shí)間：2020-03-23 15:35:07

優(yōu)質(zhì)解答

證明：
(1+1/cosx+tanx)/(1+1/cosx-tanx)
=(cosx/cosx+1/cosx+sinx/cosx)/(cosx/cosx+1/cosx-sinx/cosx)
分子分母同時(shí)乘以cosx
=(cosx+1+sinx)/(cosx+1-sinx)
分子分母同時(shí)乘以cosx
=(cos²x+cosx+sinxcosx)/[cosx*(cosx+1-sinx)]
=(1-sin²x+cosx+sinxcosx)/[cosx*(cosx+1-sinx)]
=[(1-sinx)(1+sinx)+cosx(1+sinx)]/[cosx*(cosx+1-sinx)]
=(1+sinx)(1-sinx+cosx)/[cosx*(cosx+1-sinx)]
=(1+sinx)/cosx
∴ 等式成立.