Simplify sin(15)cos(15)+cos(15)sin(15)

Problem

sin(15)*cos(15)+cos(15)*sin(15)

Solution

1. Identify the expression as a sum of two identical terms.

sin(15)*cos(15)+cos(15)*sin(15)=2*sin(15)*cos(15)

2. Apply the double angle formula for sine, which states sin(2*θ)=2*sin(θ)*cos(θ)

θ=15

3. Substitute the value of θ into the formula.

2*sin(15)*cos(15)=sin(2⋅15)

4. Multiply the values inside the sine function.

sin(30)

5. Evaluate the sine of 30 using the unit circle or standard trigonometric values.

sin(30)=1/2

Final Answer

sin(15)*cos(15)+cos(15)*sin(15)=1/2

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