解：$(1)\frac {sin 30°}{cos 30°}=\frac 12÷\frac {\sqrt 3}2=\frac {\sqrt 3}3=tan 30°$
对于任意锐角α，都有$\frac {sin α}{cosα}=tan α$
理由：如图，$sin α=\frac ac，$$cos α=\frac bc，$$tan α=\frac ab$
∴$\frac {sin α}{cos α}=\frac ac÷\frac bc=\frac ab=tan α$
$(2)①cos^2 45°+sin^2 45°=(\frac {\sqrt 2}2)^2+(\frac {\sqrt 2}2)^2=\frac 12+\frac 12=1$
$②cos^2 60°+sin^2 60°=(\frac 12)^2+(\frac {\sqrt 3}2)^2=\frac 14+\frac 34=1$
发现：对于任意锐角α，都有$cos^2α+sin^2α=1$
理由：如图，$sinα=\frac ac，$$cosα=\frac bc$
$cos^2 α+sin^2 α=(\frac bc)^2+(\frac ac)^2=\frac {a^2+b^2}{c^2}=\frac {c^2}{c^2}=1$
