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, $\frac{d y}{d x}=\frac{\pi}{180} \sec \frac{x \pi}{180} \tan \frac{\pi}{180} \times$
$\Rightarrow \frac{d y}{d x}=\frac{\pi}{180} \sec x^{\circ} .\tan x^{\circ}$