Simplify tan(-( square root of 3)/3)

Problem

tan(−√(,3)/3)

Solution

1. Identify the property of the tangent function. Since tangent is an odd function, tan(−x)=−tan(x)

2. Apply the odd function property to the expression.

tan(−√(,3)/3)=−tan(√(,3)/3)

3. Recognize the value of the tangent function at the standard angle. The value √(,3)/3 is equivalent to 1/√(,3)

4. Determine the angle whose tangent is 1/√(,3) In the first quadrant, tan(π/6)=1/√(,3)

5. Substitute the known value into the expression.

−tan(π/6)=−√(,3)/3

Final Answer

tan(−√(,3)/3)=tan(−√(,3)/3)

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