Question\text{هرگاه } x \text{ باشد، بیشترین مقدار } \tan x + \cot x \text{ کدام است؟}

Studdy Solution
Evaluate $\frac{1}{\sin x \cos x}$ at the critical points:
For $x = \frac{\pi}{4}$:
$$\sin x = \cos x = \frac{\sqrt{2}}{2}$$
$$\sin x \cos x = \left(\frac{\sqrt{2}}{2}\right)^2 = \frac{1}{2}$$
Thus,
$$\frac{1}{\sin x \cos x} = \frac{1}{\frac{1}{2}} = 2$$
The maximum value of $\tan x + \cot x$ is:
$$\boxed{2}$$