MCQ practice · SSC Higher Mathematics Board questions · Chapter 8: Trigonometry
In △ABC, what is sec((A + B)/2)?
Think it through first, then pick an option.
- a cosec π/2
- b sec π/2
- c sec C/2
- d cosec C/2
Answer and explanation
Correct answer: d cosec C/2
(A + B)/2 = (π − C)/2 = π/2 − C/2; sec(π/2 − C/2) = cosec(C/2).
Why the other options are wrong
- a cosec π/2: cosec(π/2) = 1; here the angle is not π/2 but π/2 − C/2.
- b sec π/2: sec(π/2) is undefined; here the angle is π/2 − C/2.
- c sec C/2: sec(C/2) would need the angle C/2; here (A + B)/2 = π/2 − C/2.
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