Answer:
cos(A + B) = - cosC
Explanation:
using the addition identity
cos(x ± y) = cosxcosy ∓ sinxsiny
given
A + B + C = π ( subtract C from both sides )
A+ B = π - C
then
cos(A + B)
= cos(π - C)
= cosπ cosC + sinπ sinC
= - 1 × cosC + 0 × sinC
= - cosC + 0
= - cosC