左式上下同乘(cosx+sinx+1),则
(cosx+sinx+1)^2
左式=-------------------
(cosx+1)^2-(sinx)^2
(cosx)^2+(sinx)^2+1+2cosx+2sinx+2sinxcosx
=-----------------------------------------
(cosx)^2+1+2cosx-(sinx)^2
2[1+cosx+sinx+sinxcosx]
=-----------------------
2[(cosx)^2+cosx]
(1+cosx)(1+sinx)
=----------------
cosx(cos+1)
1+sinx
=------
cosx
=右式