Question

The slope of the tangent to the curve $x=\sec y$ at the point $y={\sec }^{-1}(-2)$ is

• A. $\frac{1}{2\sqrt{3}}$
• B. $\frac{-1}{2\sqrt{3}}$
• C. $\frac{1}{4\sqrt{3}}$
• D. none of these

Answer 1

The correct option is B $\frac{-1}{2\sqrt{3}}$

Given, $x=\sec y$

$\Rightarrow dx=\sec y.\tan ydy$
$\Rightarrow \frac{dy}{dx}=\frac{1}{\sec y.\tan y}$
Hence required slope is, $=\frac{1}{(-2).\sqrt{(-2{)}^2-1}}=-\frac{1}{2\sqrt{3}}$