The conjecture of this problem is that the equilateral triangle is obviously established, and the following formal process is adopted:

a/cosA=b/cosB→acosB=bcosA

According to the projective theorem, acosB+bcosA=c

Therefore, c = 2 acosb. ...

Pay attention to the symmetry of a, b and c, and you can get

a=2ccosB……②

From ① and ②,

c=4c(cosB)^2

COSB = 1/2.

The simple discussion is correct.

Similarly, A=B=C=60 can be obtained.