Question

$\frac{d}{dx}\left({\sec }^{2}x+{\mathrm{cosec}}^{2}x\right)=$

• A. $-4\sec x\cdot \tan x\cdot \cos ecx\cdot \cot x$
• B. $4\sec x\cdot \cos ecx$
• C. $2\sec x\cdot \tan x-2\cos ecx\cdot \cot x$
• D. $2{\sec }^2\cdot \tan x-2{\mathrm{cosec}}^{2}x\cdot \cot x$

Answer 1

The correct option is D $2{\sec }^2\cdot \tan x-2{\mathrm{cosec}}^{2}x\cdot \cot x$

Let, $f\left(x\right)={\sec }^2+\cos e{c}^{2}x$

$\frac{d}{dx}f\left(x\right)=2\sec x.\sec x\tan x\cos e{x}^{2}x+{\sec }^{2}x2\cos exx(-cosecx\cot x)$

$=2{\sec }^{2}x\cdot \tan x-2{\mathrm{cosec}}^{2}x\cdot \cot x$