If sin 2θ = 2 sin θ cos θ, what is the value of sin 2(30°)?

If sin 2θ = 2 sin θ cos θ, what is the value of sin 2(30°)?

Step 1: Identify the angle given in the question, which is 30°.
Step 2: Use the formula for sin 2θ, which states that sin 2θ = 2 sin θ cos θ.
Step 3: Substitute θ with 30° in the formula: sin 2(30°) = 2 sin(30°) cos(30°).
Step 4: Find the values of sin(30°) and cos(30°). We know that sin(30°) = 1/2 and cos(30°) = √3/2.
Step 5: Substitute these values into the equation: sin 2(30°) = 2 * (1/2) * (√3/2).
Step 6: Simplify the equation: sin 2(30°) = 2 * (1/2) * (√3/2) = (1) * (√3/2) = √3/2.
Step 7: Recognize that sin 60° is equal to √3/2, confirming that sin 2(30°) = sin 60°.

Double Angle Identity – The question tests the understanding of the double angle identity for sine, which states that sin 2θ = 2 sin θ cos θ.
Trigonometric Values – It also tests the knowledge of specific trigonometric values, particularly sin 30° and sin 60°.