Question

If $f\left(tanx\right)=cos2x,x\ne (2n+1)\frac{\pi }{2},n\in I$ then incorrect statement is

• A. $f\left(x\right)$ is an even function
• B. $f\left(x\right)$ is an odd function
• C. Range of $f\left(x\right)$ is $\left[-1,1\right]$
• D. Domain of $f\left(x\right)$ is $x\in R$

Answer 1

Answer: (B)

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

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