Recognize that the expression involves the sine of an angle, specifically sin(15°). To find the exact value, use the angle subtraction identity for sine: sin(a - b) = sin(a)cos(b) - cos(a)sin(b).
Choose angles a = 45° and b = 30° because 15° = 45° - 30°. This allows us to use known values: sin(45°) = √2/2, cos(45°) = √2/2, sin(30°) = 1/2, and cos(30°) = √3/2.
Substitute these values into the identity: sin(15°) = sin(45° - 30°) = sin(45°)cos(30°) - cos(45°)sin(30°).
Calculate each term: sin(45°)cos(30°) = (√2/2)(√3/2) and cos(45°)sin(30°) = (√2/2)(1/2).
Combine the results: sin(15°) = (√2/2)(√3/2) - (√2/2)(1/2). Simplify the expression to find the exact value of sin(15°).