Multiple choice

(\text{If } 2\sin(3x - 15)° = 1, 0° < (3x - 15) < 90°, \text{ then find the value of } \cos^2(2x + 15)° + \cot^2 (x + 15)°)

  1. $\(\frac{7}{2}\)$
  2. $\(\frac{5}{25}\)$
  3. $\(1\)$
  4. $\(-\frac{7}{2}\)$
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A Correct answer
Explanation

2sin(3x-15) = 1, so sin(3x-15) = 1/2. Since 0° < (3x-15) < 90°, we have (3x-15) = 30°, so 3x = 45°, x = 15°. Then cos²(2x+15) = cos²(45°) = (1/√2)² = 1/2. And cot²(x+15) = cot²(30°) = (√3)² = 3. Sum = 1/2 + 3 = 7/2. The key is solving for x using the principal value of sine in the first quadrant.

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