The minimum value of 9 t a n 2 θ + 4 c o t 2 θ is Options: A . &nbsp 13 B . &nbsp 9 C . &nbsp 6 D . &nbsp 12

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

Discussion Forum : Trigonometric Functions

Question -

The minimum value of $9 t a n^{2} θ + 4 c o t^{2} θ$ is

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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