若(1+sinx)/cosx=-1/2,则cos/sinx-1=
问题描述:
若(1+sinx)/cosx=-1/2,则cos/sinx-1=
答
(1+sinx)/cosx=-1/2(1+sinx)cosx/(cosx*cosx)=-1/2(1+sinx)cosx/(cosx)^2=-1/2(1+sinx)cosx/[1-(sinx)^2]=-1/2(1+sinx)cosx/[(1-sinx)(1+sinx)]=-1/2cosx/(1-sinx)=-1/2cosx/(sinx-1)=1/2