Problem 0001
If cosA + cosB+ cosC= 0 , prove that cos3A +cos3B+cos3C=12cosAcosBcosC
Answer:
cosA = x, cosB = y, cosC = z
x + y + z = 0
x3 + y3 + z3 = 3xyz
Now, cos3A + cos3B + cos3C
= 4(x3 + y3 +z3) – 3(x+y+z) = 4(3xyz) – 3.0 = 12xyz
= 12 cosA.cosB.cosC. (proved)
