Simplify

Problem

sin(π/6)*cos((2*π)/3)+cos(π/6)*sin((2*π)/3)

Solution

1. Identify the trigonometric identity that matches the structure of the expression.

2. Apply the sine addition formula, which states sin(A+B)=sin(A)*cos(B)+cos(A)*sin(B)

3. Substitute the values A=π/6 and B=(2*π)/3 into the formula.

sin(π/6+(2*π)/3)

4. Find a common denominator to add the angles inside the sine function.

π/6+(4*π)/6=(5*π)/6

5. Evaluate the resulting sine value using the unit circle.

sin((5*π)/6)=1/2

Final Answer

sin(π/6)*cos((2*π)/3)+cos(π/6)*sin((2*π)/3)=1/2

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