Question

Prove that cosA + cos(A + 120°) + cos” (A – 120°) = 3/2
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Answer 1

Cos 2A + 1 = 2 Cos 2 ( A )  

(1 + Cos 2A)  /2 = Cos 2A

i.e  Cos 2A = (1 + Cos 2A)/2

${array}{l}{\frac{1+\cos (2(A-120))}{2}+\cos 2 A+\frac{1+\cos (2(A+120))}{2}}\\ {\frac{1+\cos ((2 A-240))+1+1+\cos ((2 A+240))}{2}+\cos 2 A}\\ {1+\frac{\cos ((2 A-240))+1+1+\cos ((2 A+240))}{2}+\cos 2 A}\\ {1+\frac{2 \cos 2 A \cos 240}{2}+\cos 2 A}{array}$

1 + Cos2 A( -1/2  ) + Cos2 A

1- ( 2 Cos 2A -1) (  1/2  ) + Cos2A

1 – Cos2A + (  1/2  ) + Cos2 A

= 3/2

Answer 2

Answer:

proved cos A = 120°π+ACod