Answer:
(√2)/2
Explanation:
A right triangle with one acute angle equal to 45° will also have the other acute angle equal to 45°. The angles being equal means the legs will be equal. If we assign each leg the length 1, then the Pythagorean theorem tells us the hypotenuse is length ...
√(1^2 +1^2) = √2
The cosine of the acute angle is the ratio of the nearest leg length (1) to the hypotenuse length (√2), so the exact value of the cosine is ...
cos(45°) = 1/√2 = (√2)/2
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(√2)/2 is the fraction with the denominator "rationalized". Sometimes, that is the preferred presentation of this number.