Question

In a triangle prove cos c=cos(a+b)

Answer 1

we know a+b+c=180
a+b=180-c
take cos both side
cos (a+b)=cos(180-c)
cos (a+b)=-cos c

Answer 2

In a triangle, we know that A+B+C=180
C=180-(A+B)
Cos(C)=Cos[180-(A+B)]
Cos(C)=-Cos(A+B)
Cos(C) is equal to -Cos(A+B) in a triangle but not Cos(A+B).
Hope you find this answer helpful.