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Prove that: cos^2A+cos^2(A+pi/3)+cos^2(A...

Prove that: `cos^2A+cos^2(A+pi/3)+cos^2(A-pi/3)=3/2`

A

0

B

`1/2`

C

`3/2`

D

1

Text Solution

Verified by Experts

The correct Answer is:
C
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Prove that : cos^(2)A+cos^(2)(A+pi/3)+cos^(2)(A-pi/3) =1/2[2cos^(2)A+2cos^(2)(A+60^(@))+2cos^(2)(A-60^(@))] =1/2[1+cos2A+1+cos(2A+120^(@))+1+cos(2A-120^(@))] 1/2[3+cos2A+cos(2A+120^(@))+cos(2A-120^(@))] 1/2[3+cos2A+2cos(2A+120^(@)+2A-120^(@))/(2).cos(2A+120^(@)-2A+120^(@))/(2)] =1/2[3+cos2A+2cos2Acos120^(@)] =1/2[3cos2A+2cos2Acos(90^(@)+30^(@))] =1/2[3+cos2A-2.cos2A.(1/2)] =1/2(3+cos2A-cos2A) =3/2 = RHS Hence Proved.

Prove that: cos^(2)A+cos^(2)(A+(pi)/(3))+cos^(2)(A-(pi)/(3))=(3)/(2)

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cos^(^^)2A+cos^(^^)2(A+2pi/3)+cos^(^^)2(A-2pi/3)=3/2 OR cos^(^^)2A+cos^(^^)2(A+pi/3)+cos^(^^)2(A-pi/3)=3/2

Prove that : cos A+cos(A+(2 pi)/(3))+cos(A+(4 pi)/(3))=0

Prove that cos^(2)x+cos^(2)(x+(pi)/(3))+cos^(2)(x-(pi)/(3))=(3)/(2)

Prove that cos^(2)x+cos^(2)(x+(pi)/(3))+cos^(2)(x-(pi)/(3))=(3)/(2)

Prove that: cos^(3)A + cos^(3)((2pi)/(3)+A) + cos^(3)((4pi)/3+A) = 3/4 cos3A

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TARGET PUBLICATION-FACTORIZATION FORMULAE-CRITICAL THINKING
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  10. If A+B+C=pi , prove that cos 2A +cos 2B +cos 2C=-1-4cos A cos Bcos ...

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  12. If A+B+C=3pi/2. Then cos 2A +cos 2B+cos2C is equal to

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  15. Prove that: cos^2A+cos^2(A+pi/3)+cos^2(A-pi/3)=3/2

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