To prove the equation sin(a + 30°) - sin(a - 30°) = cos(a), we use the sum and difference formulas for sine. After applying these formulas, it simplifies to cos(a), confirming that option C is the correct method to use.
To prove that sin(a + 30°) - sin(a - 30°) = cos(a), we can use the sum and difference formulas for sine, which are formula number 10 in the list you provided. Applying the formulas, we have:
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- sin(a + 30°) = sin(a)cos(30°) + cos(a)sin(30°)
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- sin(a - 30°) = sin(a)cos(30°) - cos(a)sin(30°)
Subtracting the second equation from the first, we get:
sin(a + 30°) - sin(a - 30°) = (sin(a)cos(30°) + cos(a)sin(30°)) - (sin(a)cos(30°) - cos(a)sin(30°))
This simplifies to:
2cos(a)sin(30°) = cos(a)(2sin(30°)) = cos(a)(2 * 1/2) = cos(a)
Thus, proving the given equation. Therefore, the correct answer is C. By using the sum and difference formula for sine.