Multiple choice

What is the value of [sin(90°-

    • cos(180°-2A)]/[cos(90° - 2A) + sin(180°- A)]?

  2. Sin(A/2).cosA

  3. Cot(A/2)

  4. Tan(A/2)

  5. sinA.cos(A/2)
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Using reduction formulas: sin(90°-A) = cosA, cos(180°-2A) = -cos2A, cos(90°-2A) = sin2A, sin(180°-A) = sinA. Expression = (cosA - cos2A)/(sin2A + sinA). Using sum-to-product: cosA - cos2A = 2sin(3A/2)sin(A/2) and sin2A + sinA = 2sin(3A/2)cos(A/2). Ratio = sin(A/2)/cos(A/2) = tan(A/2). Options A, B, and D are incorrect results.

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