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SSC CHSL 2022 · PYQ · Trigonometry · medium

If cot 75° = 2 − √3. Find the value of cot 15°.

Answer

The correct answer is A: 2 + √3. cot 15° = cot(90° − 75°) = tan 75°. Since tan 75° = 1/cot 75° = 1/(2−√3) = (2+√3)/((2−√3)(2+√3)) = (2+√3)/(4−3) = 2+√3.

  1. A.2 + √3✓ Correct
  2. B.√3 + 1
  3. C.√3 − 1
  4. D.2 − √3

Explanation

cot 15° = cot(90° − 75°) = tan 75°. Since tan 75° = 1/cot 75° = 1/(2−√3) = (2+√3)/((2−√3)(2+√3)) = (2+√3)/(4−3) = 2+√3.
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