The minimum value of 9 t a n 2 θ + 4 c o t 2 θ is Options: A . &nbsp13 B . &nbsp9 C . &nbsp6 D . &nbsp12

Answer: Option D : D A.M. ≥ G.M. ⇒ 9 t a n 2 θ + 4 c o t 2 θ 2 ≥ √ 4 c o t 2 θ . 9 t a n 2 θ ⇒ 9 t a n 2 θ + 4 c o t 2 θ ≥ 12 Therefore, the minimum value is 12.

The minimum value of 9tan2θ+4cot2θ is

Question

The minimum value of

9 t a n^{2} θ + 4 c o t^{2} θ

Options:

A . 13

B . 9

C . 6

D . 12

Answer: Option D
:
D
A.M.

\geq

G.M.

\Rightarrow

\frac{9 t a n^{2} θ + 4 c o t^{2} θ}{2}

\geq

\sqrt{4 c o t^{2} θ . 9 t a n^{2} θ}

\Rightarrow

9 t a n^{2} θ + 4 c o t^{2} θ

\geq

12
Therefore, the minimum value is 12.

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