Question

find the minimum value of 16cotx+9tanx​

Answer 1

it's simple mate

just convert cotx into tan x

16/tanx + 9tanx = (9tan²x +16)/tan x

the for minimum value of the expression tan x should be 1

25

Answer 2

Step-by-step explanation:

We know that AM is greater than or equal to GM.

So,

$\frac{16 \: cot \: x + 9 \: tan \: x}{2} \geqslant \sqrt{16 \: cot \: x \: 9 \: tan \: x} \\ \frac{16 \: cot \: x + 9 \: tan \: x}{2} \geqslant \sqrt{16 \times 9} \\ 16 \: cot \: x + 9 \: tan \: x \geqslant 2 \times 4\times 3 \\ 16 \: cot \: x + 9 \: tan \: x \geqslant 24$

So, maximum value is 24.

Thank you