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Prove that: cos Acos(60^0-A)cos(60^0+A)=...

Prove that: `cos Acos(60^0-A)cos(60^0+A)=1/4cos3A`

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`cos A cos (60-A) cos (60+A)=frac{cos 3 A}{4}`

`cos (x-y) cos (x+y)=cos ^{2} y-sin ^{2} x`

`cos 3 x=4 cos ^{3} x-3 cos x`

`cos A cos (60-A) cos (60+A)`

`=cos A(cos ^{2}(A)-sin ^{2} 60)`

`=cos A(cos ^{2} A-frac{3}{4})`

`=frac{4 cos 3 A-3 cos A}{4}`

`=frac{cos 3 A}{4}`

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