Question

If $y=\sec x^{\circ }$, then $\frac{dy}{dx}$ is equal to :

• A. $\sec x\tan x$
• B. $\sec x^{\circ }\tan x^{\circ }$
• C. $\frac{\pi }{180}\sec x^{\circ }\tan x^{\circ }$
• D. None of these

Answer 1

Answer: (C)

Let $y=\sec x^{\circ }$
Now, $x^{\circ }=\frac{\pi }{180}.x$
$\therefore y=\sec \frac{\pi }{180}x$
Now, $\frac{dy}{dx}=\frac{\pi }{180}\sec \frac{x\pi }{180}\tan \frac{\pi }{180}\times$
$\Rightarrow \frac{dy}{dx}=\frac{\pi }{180}\sec x^{\circ }.\tan x^{\circ }$