y=sinx+2cosx
=√5(sinxcosa+cosxsina)
=√5sin(x+a)
当x+a=2kπ+π/2时,y取得最大值
cosa=√5/5；sina=2√5/5
tanx=tan(2kπ+π/2-a)=cota
=cosa/sina
=1/2