Question

The equation of normal to the curve y = tanx at (0, 0) is ______.

Answer 1

The equation of normal to the curve y = tanx at (0, 0) is y + x = 0.

Explanation:

We have y = tan x.

So, `"dy"/"dx" = sec^2x`

∴ Slope of the normal = `(-1)/(sec^2x) = - cos^2x`

At the point (0, 0) the slope = `- cos^2(0)` = –1

So the equation of normal at (0, 0) is y – 0 = –1(x – 0)

⇒ y = – x

⇒ y + x = 0

Hence, the required equation is y + x = 0.