Question

The equation of normal to the curve $y=\tan x$ at the point $(0,0)$ is -

• A. $x+y=0$
• B. $x-y=0$
• C. $x+2y=0$
• D. None of these

Answer 1

The correct option is A $x+y=0$

$y=\tan x$
$\Rightarrow \frac{dy}{dx}=\sec x$
$\Rightarrow \therefore {\left(\frac{dy}{dx}\right)}_{(0,0)}=1=m$ (say)
$\therefore$ Slope of normal at the given point is $=-\frac{1}{m}=-1$
Therefore, equation of normal is, $(y-0)=-1(x-0)$
$\Rightarrow x+y=0$
Hence, option 'A' is correct.