Multiple choice

(\text{If } \sin 3A = \cos(30^\circ - A), \text{ where A is an acute angle, then what is the value of } 2\csc A + \tan^2 2A - \cot^2 A)

  1. $\(\frac{17}{2}\)$
  2. $\(4\)$
  3. $\(5\)$
  4. $\(\frac{7}{4}\)$
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B Correct answer
Explanation

Using complementary angle identity sin θ = cos(90° - θ), we have sin 3A = cos(90° - 3A). Equating with cos(30° - A): 90° - 3A = 30° - A (valid for acute angles). Solving: 60° = 2A, so A = 30°. Then 2csc 30° + tan²(60°) - cot²(30°) = 2(2) + (√3)² - (√3)² = 4 + 3 - 3 = 4.

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