(sinA)^2-(cosA)^2=1/2
(sinA)^2+(cosA)^2=1
因为角A为锐角
所以(sinA)^2=3/4
sinA=(根号3)/2
A=π/3
sinB+sinC
=sin(2π/3-C)+sinC
=sin2π/3cosC-sinCcos2π/3+sinC
=(sinB+sinC)/2cosC+3/2sinC
=根号3sin(C+π/6)
C属于(0,2π/3)的范围内
所以sinB+sinC小于等于根号3
即sinB+sinC小于等于2sinA
即b+c小于等于2a
(sinA)^2-(cosA)^2=1/2
(sinA)^2+(cosA)^2=1
因为角A为锐角
所以(sinA)^2=3/4
sinA=(根号3)/2
A=π/3
sinB+sinC
=sin(2π/3-C)+sinC
=sin2π/3cosC-sinCcos2π/3+sinC
=(sinB+sinC)/2cosC+3/2sinC
=根号3sin(C+π/6)
C属于(0,2π/3)的范围内
所以sinB+sinC小于等于根号3
即sinB+sinC小于等于2sinA
即b+c小于等于2a