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MCQ practice · SSC Higher Mathematics Board questions · Chapter 8: Trigonometry

Dinajpur Board 2024

If cotA and cosecA have opposite signs, what is cosecA?

Think it through first, then pick an option.

  1. a 25/7
  2. b 24/7
  3. c −24/7
  4. d −25/7
Answer and explanation

Correct answer: d −25/7

tanA = 7/24 and cotA positive; cosecA has the opposite sign ⇒ sinA negative (3rd quadrant); cosecA = −25/7.

Why the other options are wrong

  • a 25/7: 25/7 is positive; cotA is positive and cosecA has the opposite sign, so it is negative.
  • b 24/7: 24/7 is positive and the wrong value; cosecA is of the form 25/7.
  • c −24/7: −24/7 has the wrong size; cosecA = −25/7.