Question

find the equation of the tangent to the curve y = tan x at the point (0, 0). sl = 3

Explanation:

Step1: Find the derivative of y

The derivative of $y = \tan x$ is $y'=\sec^{2}x$.

Step2: Evaluate the derivative at the given point

Substitute $x = 0$ into $y'$. Since $\sec x=\frac{1}{\cos x}$, when $x = 0$, $\cos(0)=1$, so $\sec(0) = 1$ and $y'(0)=\sec^{2}(0)=1$. The slope $m$ of the tangent line is 1.

Step3: Use the point - slope form of a line

The point - slope form is $y - y_1=m(x - x_1)$. Here, $(x_1,y_1)=(0,0)$ and $m = 1$. So $y-0=1\times(x - 0)$.

Answer:

$y=x$