在ABC中,若a^2+b^2=2c^2.求sina^2+sin^2b/sin^2 c
问题描述:
在ABC中,若a^2+b^2=2c^2.求sina^2+sin^2b/sin^2 c
答
a/sinA=c/sinC所以a/c=sinA/sinC同理b/c=sinB/sinCa^2+b^2=2c^2a^2/c^2+b^2/c^2=2所以(a/c)^2+(b/c)^2=2所以(sinA/sinC)^2+(sinB/sinC)^2=2所以[(sinA)^2+(sinB)^2]/(sinC)^2=2