Application of Derivatives — Class 12 Maths Solution

The equation of normal to the curve $y = \tan x$ at (0,0) is $x + y = 0$.
$y = \tan x \Rightarrow \frac{{dy}}{{dx}} = {\sec ^2}x$

$\Rightarrow$ ${\left( {\frac{{dy}}{{dx}}} \right)_{(0,0)}} = {\sec ^2}0 = 1$ and $- \frac{1}{{\left( {\frac{{dy}}{{dx}}} \right)}} = - \frac{1}{1}$

Therefore the equation of normal to the curve $y = \tan x$ at (0,0) is
$y - 0 = - 1(x - 0)$

$\Rightarrow$ $y + x = 0$