Question

Let A, B, C be the angles of a triangle, so that A + B + C = pi. Show that cos(A+B) = -cosC

Answer 1

subtract C from both side ..u will get

Answer 2

\[\huge A+B=\pi-c\]

Answer 3

now take cosine both side

Answer 4

\[\huge \cos (\pi-C) =-cosC\]

Answer 5

cos(A+B)+cos(C)=0
cos(A+B)+cos(c)=0

2 cos ((A+B+C)/2) cos ( (A+B-C)/2)=0
cos ((A+B+C)/2) = cos(pi/2) =0 done :)