Question

在ABC中,若a^2+b^2=2c^2.求sina^2+sin^2b/sin^2 c

Answer 1

a/sinA=c/sinC

所以a/c=sinA/sinC

同理

b/c=sinB/sinC

a^2+b^2=2c^2

a^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