Question

Prove that cos55°+cos65°+cos175°= 0

Answer 1

Sum-to-product identity: .cosA+cosB=2⋅cos(A+B2)cos(A−B2)


We have: cos55o+cos65o+cos175o⏟

. . . . .=cos55o+⏞2⋅cos120ocos55o

. . . . .=cos55o+2(−12)cos55o

. . . . .=cos55o−cos55o

. . . . .=0