Question

please solve this class 9 question .
Prove that cos^2(A – 120°) + cos^2 A + cos^2(A + 120°) = 3/2​

Answer 1

Answer:

cos22A+cos22(A+120∘)+cos22(A−120∘)=32cos22A+cos22(A+120∘)+cos22(A−120∘)=32

We know that

cos2A=1+cos2A2cos2A=1+cos⁡2A2 ..............(i)

cos22(A+120∘)=1+cos(2A+240∘)2cos22(A+120∘)=1+cos⁡(2A+240∘)2 ..............(ii)

And cos22(A−120∘)=1+cos(2A−240∘)2cos22(A−120∘)=1+cos⁡(2A−240∘)2..............(iii)

Adding all these three equations,

cos22A+cos22(A+120∘)+cos22(A−120∘)cos22A+cos22(A+120∘)+cos22(A−120∘) = 32+1+cos2A2+1+cos(2A+240∘)2+1+cos(2A−240∘)232+1+cos⁡2A2+1+cos⁡(2A+240∘)2+1+cos⁡(2A−240∘)2

= 3+1+cos2A+1+cos(2A+240∘)+1+cos(2A−240∘)23+1+cos⁡2A+1+cos⁡(2A+240∘)+1+cos⁡(2A−240∘)2

= 3+3+cos2A+cos(2A+240∘)+cos(2A−240∘)23+3+cos⁡2A+cos⁡(2A+240∘)+cos⁡(2A−240∘)2

= 3+3+cos2A+2cos2A.cos240∘23+3+cos⁡2A+2cos⁡2A.cos⁡240∘2

= 3+3+cos2A−cos2A23+3+cos⁡2A−cos⁡2A2

= 6262

⇒⇒ cos22A+cos22(A+120∘)+cos22(A−120∘)=32

i will sure its answer is right but please brainlist mark me