In an acute angled ΔABC, the least value of sec A + sec B + sec C is:
In an acute triangle, all the cosines are positive and sec is convex on \((0, \frac{\pi}{2})\). By Jensen's inequality (or AM-HM with \(\cos A + \cos B + \cos C \le \frac{3}{2}\)):
\(\sec A + \sec B + \sec C \ge \frac{9}{\cos A + \cos B + \cos C} \ge \frac{9}{3/2} = 6\)
Equality holds for the equilateral triangle, where each sec 60° = 2.
Least value = 6.
Answer: (A) 6
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