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

Problem

tan(π/3−π/6)

Solution

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

π/3=(2*π)/6

2. Subtract the angles.

(2*π)/6−π/6=π/6

3. Rewrite the expression using the simplified angle.

tan(π/6)

4. Identify the exact value of the tangent function at π/6 (or 30 from the unit circle.

tan(π/6)=√(,3)/3

Final Answer

tan(π/3−π/6)=√(,3)/3

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