#a+b+c=180^@#,
#LHS=cos(b+c-a)+cos(c+a-b)+cos(a+b-c)#
#=cos(180-2a)+cos(180-2b)+cos(180-2c)#
#=-cos(2a)-cos(2b)-cos(2c)#
#=-(2cos^2(a)-1)-(cos(2b)+cos(2c))#
#=1-2cos^2(a)-(2cos(b+c)cos(b-c))#
#=1-2cos^2(a)-2cos(180-a)cos(b-c)#
#=1-2cos^2(a)+2cos(a)cos(b-c)#
#=1-2cos(a)(cos(a)-cos(b-c))#
#=1-2cos(a)(cos(180-(b+c))-cos(b-c))#
#=1-2cos(a)(-cos(b+c)-cos(b-c))#
#=1+2cos(a)(cos(b+c)+cos(b-c))#
# =1+4cos(a)cos(b)cos(c)#