Question

The value of $\underset{x\to \pi /4}{lim}\frac{{\tan }^{2}x-\tan x}{\cos (x+\frac{\pi }{4})}$ is

• A. $8$
• B. $4$
• C. $-8$
• D. $-2$

Answer 1

The correct option is D $-2$

Let $L={lim}_{x\to \pi /4}\frac{{\tan }^{2}x-\tan x}{\cos (x+\frac{\pi }{4})}$

Using L' Hospital rule, we get,

$L={lim}_{x\to \pi /4}\frac{2\tan x{\sec }^{2}x-{\sec }^{2}x}{-\sin (x+\pi /4)}=\frac{2\left(1\right)\left(2\right)-\left(2\right)}{-\left(1\right)}=-2$

Hence, this is the answer.