Simplify cos(arccos(-( square root of 3)/2))

Problem

cos(arccos(−√(,3)/2))

Solution

1. Identify the composition of a trigonometric function and its inverse. The expression is of the form cos(arccos(x))

2. Apply the property of inverse functions. For any value x in the domain of the inverse cosine function, which is [−1,1] the identity cos(arccos(x))=x holds true.

3. Verify the domain of the input value. The value x=−√(,3)/2 is approximately −0.866 which falls within the interval [−1,1]

4. Evaluate the expression by applying the identity directly.

Final Answer

cos(arccos(−√(,3)/2))=−√(,3)/2

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