If a+b+c=pi find cos(a+b)+cos c.. how to do this ?

Answer 1

Have a look at the cosine wave graph. Can you see by symmetry that cos x = - cos (pi - x)? Therefore cos (a + b) + cos c = cos (a + b) + - cos (180 - c) = cos (a + b) - cos (a + b) = 0.

Answer 2

a + b + c = pi

a + b = pi - c

cos(a + b) = cos(pi - c)

From trigonometric compound angle formulas cos(A - B)  = cosA cosB + sinA sinB

cos(a + b) = cos(pi) cos(c) + sin(pi) sin(c)

cos(a + b) = (-1)cos(c) + (0)sin(c)

cos(a + b) = -cos(c)

cos(a + b) + cos(c) = 0.