Simplify arccot(- square root of 5)

Problem

arccot(−√(,5))

Solution

1. Identify the range of the inverse cotangent function. By standard convention, the range of y=arccot(x) is (0,π)

2. Apply the property for negative arguments in the inverse cotangent function. For x>0 the relationship is defined as:

arccot(−x)=π−arccot(x)

3. Substitute the value x=√(,5) into the identity.

arccot(−√(,5))=π−arccot(√(,5))

4. Conclude that since √(,5) is not a standard trigonometric ratio, the expression is simplified by expressing it in terms of the principal value in the second quadrant.

Final Answer

arccot(−√(,5))=π−arccot(√(,5))

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