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Q. If $f\left(tan x\right)=cos⁡2x, \, x\neq \left(\right.2n+1\left.\right)\frac{\pi }{2}, \, n\in I$ then incorrect statement is

NTA AbhyasNTA Abhyas 2020

Solution:

$\because \frac{1 - tan^{2} x}{1 + tan^{2} x}=cos2x$

Let, $tanx=t$
$\therefore f\left(t\right)=\frac{1 - t^{2}}{1 + t^{2}}$
$\therefore f\left(x\right)=\frac{1 - x^{2}}{1 + x^{2}}$