Simplify cos(-( square root of 2)/2)

Problem

cos(−√(,2)/2)

Solution

1. Identify the nature of the expression. The task asks to evaluate the cosine of a specific numerical value, −√(,2)/2

2. Apply the even-odd property of the cosine function, which states that cos(−x)=cos(x)

3. Rewrite the expression using this property.

cos(−√(,2)/2)=cos(√(,2)/2)

4. Approximate the value if a decimal is required, or leave it in its exact form. Since √(,2)/2≈0.7071 radians, we evaluate the cosine of this value.

cos(0.7071)≈0.7602

Final Answer

cos(−√(,2)/2)=cos(√(,2)/2)

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