Explanation: 
Another Explanation (5):
দেওয়া আছে, \( f(x) = \frac{1-x^2}{1+x^2} \)
এখন, \( f(\tan x) \) এর মান নির্ণয় করতে হবে।
\( f(\tan x) = \frac{1 - (\tan x)^2}{1 + (\tan x)^2} \)
আমরা জানি, \( \tan x = \frac{\sin x}{\cos x} \)
সুতরাং, \( f(\tan x) = \frac{1 - \frac{\sin^2 x}{\cos^2 x}}{1 + \frac{\sin^2 x}{\cos^2 x}} \)
\( = \frac{\frac{\cos^2 x - \sin^2 x}{\cos^2 x}}{\frac{\cos^2 x + \sin^2 x}{\cos^2 x}} \)
\( = \frac{\cos^2 x - \sin^2 x}{\cos^2 x + \sin^2 x} \)
আমরা জানি, \( \cos^2 x + \sin^2 x = 1 \) এবং \( \cos^2 x - \sin^2 x = \cos 2x \)
সুতরাং, \( f(\tan x) = \frac{\cos 2x}{1} \)
\( = \cos 2x \)
অতএব, \( f(\tan x) = \cos 2x \) 😎
