Simplify sin(20)cos(10)+cos(20)sin(10)

Problem

sin(20)*cos(10)+cos(20)*sin(10)

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=20 and B=10 into the formula.

4. Simplify the expression by adding the angles inside the sine function.

5. Evaluate the resulting trigonometric value.

Final Answer

sin(20)*cos(10)+cos(20)*sin(10)=1/2

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