Question

13 15. Prove that : cos (120° - A) + cos A + cos (120° + A) = 0.​

Answer 1

Step-by-step explanation:

cosA+cosA(120°-A)+cosA(120°+A)

cosA+2cosA.cosA

cosA+2cosA(-cos60°)

cosA-2cosA.1/2=0

Answer 2

Answer:

We know that:

1. cos(x+y) = cosx.cosy - sinx.siny
2. cos(x-y) = cosx.cosy + sinx.siny
3. cos(120) = cos (π -60) = -cos60 =-1/2
4. sin(120) = sin(π-60) = sin60 = √3/2

Now,

cos(120 + A) = cos120.cosA - sin120.sinA

= -1/2(cosA +√3.SinA)

cos(120-A) = -1/2(cosA - √3.sinA)

LHS: cos(120-A) + cos(120+A) + cosA

= -1/2(cosA - √3sinA) - 1/2(cosA +√3.SinA) + cosA

= (2. -1/2 . cosA) + cosA

= -cosA + cosA = 0 = RHS (PROVED)