The least value of 4cosec^2 α + 9sin^2 α is:

We know that cosecα = 1/ sinα , hence applying A.M ≥ G.M logic, we get
A.M of given equation = (4 cosec$$2$$α + 9 sin$$^2$$α) / 2 …. (1)
G.M of given equation = √ (4 cosec$$^2$$α . 9 sin$$^2$$α )
= $$\sqrt{4 * 9}$$
= $$\sqrt{36}$$ = $$6$$ …. (2)
Now, we know that A.M ≥ G. M
From equations (1) and (2) above we get,
=>(4 cosec$$^2$$α + 9 sin$$^2$$α) / 2 ≥ 6
Multiplying both sides by 2
(4 cosec$$^2$$α + 9 sin$$^2$$α) ≥ 12
The minimum value will be 12.
Option D is the correct answer.