sinx+cosx
=√2(√2/2*sinx+√2/2*cosx)
=√2(sinxcosπ/4+cosxsinπ/4)
=√2sin(x+π/4)
π/4所以x+π/4=π/4或3π/4
sin(x+π/4)最小=√2/2
这里都不取到
所以sin(x+π/4)>√2/2
所以√2sin(x+π/4)>1
所以sinx+cosx>1