Question Detail
Question
Value of (cos15°/sin15°) - (sin15°/cos15°) is:
Correct Answer
Option D is the correct answer.
Detailed Explanation
cos15°/sin15° = cot15°, sin15°/cos15° = tan15°. So expression = cot15° - tan15° = (cos²15° - sin²15°)/(sin15°cos15°) = cos30°/((1/2)sin30°) = (√3/2)/((1/2)(1/2))? Let's compute properly: cot15° - tan15° = (cos15°/sin15°) - (sin15°/cos15°) = (cos²15° - sin²15°)/(sin15°cos15°) = cos30°/((1/2)sin30°) = (√3/2)/((1/2)(1/2)) = (√3/2)/(1/4) = (√3/2) × 4 = 2√3.
Hint
Use trigonometric identities or exact values.