Since arctan 1 = A, then tan A = 1, and A = p/4.
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               cos A = cos p/4 = \/2  /2   and   sin A = sin p/4 = \/2  /2

Since arccos x = B, then cos B = x, and X = x while R = 1.                 _____
                 X² + Y² = R²  so  x² + Y² = 1   and Y² = 1 - x²  so  Y = \/1 - x²
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                          cos B = x   and    sin  B = \/1 - x²     

Now cos (A + B) = cos A cos B - sin A sin B
Subsituting in values,    __                __         ____
                           =  (\/2  /2 )(x) - (\/2  /2 )(\/1 - x²)
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                           =  x\/2     -      \/2(1 - x²)
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