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2014-12-18T19:13:02+05:30

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Cos (36 - A) (Cos (36+A) + Cos (54+A) COS(54-A)

=  1/2 * [ cos 72 + Cos 2A ] + 1/2 [ Cos 108 + Cos 2A ]
 = Cos 2A + 1/2 [ cos 72 + cos 108 ]
 = cos 2 A + 1/2 [ cos 72 + Cos (180-72) ]
 = cos 2 A + 1/2 [ cos 72 - cos 72 ]
= cos 2A

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  • Brainly User
2014-12-18T22:44:15+05:30
You have, cos(54^{o}+A)=sin(90^{o}-(54^{o}+A))=sin(36^{o}-A) and similarly cos(54^{o}-A)=sin(90^{o}-(54^{o}-A))=sin(36^{o}+A).
Then the expression becomes cos(36^{o}-A)cos(36{o}+A)+sin(36^{o}-A)sin(36^{o}+A).
This is cos((36^{o}-A)-(36^{o}+A))=cos(-2A)=cos(2A).
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