Find the Exact Value tan(pi/3-pi/6)

Problem

the tangent of open paren pi over 3 minus pi over 6 close paren

Solution

1. Find a common denominator for the fractions inside the parentheses to subtract them.

pi over 3 equals 2 pi over 6

2. Subtract the angles.

2 pi over 6 minus pi over 6 equals pi over 6

3. Rewrite the expression using the simplified angle.

the tangent of pi over 6

4. Identify the exact value of the tangent function at pi over 6 (or 30 raised to the composed with power from the unit circle.

the tangent of pi over 6 equals the fraction with numerator the square root of 3 and denominator 3

Final Answer

the tangent of open paren pi over 3 minus pi over 6 close paren equals the fraction with numerator the square root of 3 and denominator 3

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