Question

Q2
Prove that cos A + cos (120 - A) + cos (120 + A) = 0​

Answer 1

LHS = Cos(A) + cos(120-A) + cos(120+A)

=> cos(A) + cos(120)cos(A) + sin(120)sin(A) + cos(120)cos(A) - sin(120)sin(A)

=> cos(A) + 2cos(120)cos(A)

=> cos(A) + 2(-1/2)cos(A)

=> cos(A) - cos(A)

=> 0 = RHS

Predefined results used above :

• Cos(A+B) = cos(A)cos(B) - sin(A)sin(B)
• cos(A-B) = cos(A)cos(B) + sin(A)sin(B)
• cos(120) = -1/2

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