UPSC NDA Math Model Paper 2

For the three angles of a ΔABC, A + B + C = π.
∴cos‌A+cos‌B+cos‌C≤

3

2

⇒

1

cos‌A+cos‌B+cos‌C

≤

2

3

......(1)
Using the AM-HM inequality:

sec‌A+sec‌B+sec‌C

3

≥

3

1 sec‌A + 1 sec‌B + 1 sec‌C

Using equation (1), we get:
⇒ sec A + sec B + sec C ≥ 6
Therefore, the least value of sec A + sec B + sec C is 6.