Find the Exact Value sin(15)cos(15)

Problem

sin(15)*cos(15)

Solution

1. Identify the double-angle identity for sine, which states sin(2*θ)=2*sin(θ)*cos(θ)

2. Rearrange the identity to solve for the product of sine and cosine by dividing both sides by 2.

sin(θ)*cos(θ)=1/2*sin(2*θ)

3. Substitute θ=15 into the rearranged identity.

sin(15)*cos(15)=1/2*sin(2⋅15)

4. Simplify the argument of the sine function.

sin(15)*cos(15)=1/2*sin(30)

5. Evaluate the exact value of sin(30) which is 1/2

sin(15)*cos(15)=1/2⋅1/2

6. Multiply the fractions to find the final result.

sin(15)*cos(15)=1/4

Final Answer

sin(15)*cos(15)=1/4

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