Find the Exact Value sin(75)+sin(15)

Problem

sin(75)+sin(15)

Solution

1. Identify the sum-to-product formula for sine, which states sin(A)+sin(B)=2*sin((A+B)/2)*cos((A−B)/2)

2. Substitute the values A=75 and B=15 into the formula.

sin(75)+sin(15)=2*sin((75+15)/2)*cos((75−15)/2)

3. Simplify the arguments inside the trigonometric functions.

(75+15)/2=45

(75−15)/2=30

4. Evaluate the trigonometric functions at these standard angles.

sin(45)=√(,2)/2

cos(30)=√(,3)/2

5. Multiply the resulting values together.

2⋅√(,2)/2⋅√(,3)/2=√(,6)/2

Final Answer

sin(75)+sin(15)=√(,6)/2

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