无法化简。
1+tanx
=1+sinx/cosx
=cosx/cos+sinx/cosx
=(cosx+sinx)/cosx
≠cosx+sinx
如果1+tanx=cosx+sinx则
(cosx+sinx)/cosx=cosx+sinx
(cosx+sinx)/cosx-(cosx+sinx)=0
(cosx+sinx)(1/cosx-1)=0
(1) cosx+sinx=0
(√2/2)cosx+(√2/2)sinx=0
in(π/4)cosx+cos(π/4)sinx=0
in(π/4+x)=0
π/4+x=0
x=kπ-π/4
(2) 1/cosx-1=0
1/cosx=1
cosx=1
x=(2k+1)π
