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Find the exact value of the expression. sin15°
A
42−6
B
46−2
C
22−6
D
44
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Guida verificata passo dopo passo
1
Step 1: Recognize that the problem involves evaluating the exact value of sin(15°). Recall that 15° can be expressed as 45° - 30°, which allows us to use the sine difference identity: sin(a - b) = sin(a)cos(b) - cos(a)sin(b).
Step 2: Substitute a = 45° and b = 30° into the sine difference identity. This gives sin(15°) = sin(45°)cos(30°) - cos(45°)sin(30°).
Step 3: Use the known exact values of trigonometric functions for 45° and 30°. Specifically, sin(45°) = √2/2, cos(45°) = √2/2, sin(30°) = 1/2, and cos(30°) = √3/2.
Step 4: Substitute these values into the expression for sin(15°). This results in sin(15°) = (√2/2)(√3/2) - (√2/2)(1/2).
Step 5: Simplify the expression by performing the multiplications and combining terms. The result will be in the form of a fraction involving square roots, which matches one of the given answer choices.