Simplify tan(pi/4)-sin(pi/6)

Problem

tan(π/4)−sin(π/6)

Solution

1. Identify the exact value of the first trigonometric term using the unit circle or special triangles.

tan(π/4)=1

2. Identify the exact value of the second trigonometric term using the unit circle or special triangles.

sin(π/6)=1/2

3. Substitute these values back into the original expression.

1−1/2

4. Subtract the values by finding a common denominator.

2/2−1/2=1/2

Final Answer

tan(π/4)−sin(π/6)=1/2

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