Question

Least value of the expression 9sec²θ + 4cosec²θ, is-

• A. 6
• B. 1
• C. 36
• D. 25

Answer 1

Answer: (D)

25

Answer 2

9sec²θ + 4cosec²θ = 13 + 9tan²θ + 4cot²θ

By using A.M. and G.M.

13 + 9tan²θ + 4cot²θ ≥ 13 + 2$\sqrt{9\tan^{2}\theta.4\cot^{2}\theta}$

So 13 + 9tan²θ + 4cot²θ ≥ 25.