证明:cos2A/a^2-cos2B/b^2=1/a^2-1/b^2

问题描述:

证明:cos2A/a^2-cos2B/b^2=1/a^2-1/b^2

cos2A/a^2-cos2B/b^2
=(1-2sinA^2)/a^2-(1-2sinB^2)/b^2
=(1/a^2-1/b^2)+2sinB^2/b^2-2sinA^2/a^2,
由正弦定理知,a/sinA=b/sinB,
sinA/a=sinB/b
=(1/a^2-1/b^2)+2sinA^2/a^2-2sinA^2/a^2,
=1/a^2-1/b^2