Question

$\underset{x\to \frac{\pi }{4}}{lim}\frac{\cos x-\sin x}{(\frac{\pi }{4}-x)(\cos x+\sin x)}$=

• A. $2$
• B. $1$
• C. $0$
• D. $3$

Answer 1

The correct option is B $1$

$\underset{x\to \frac{\pi }{4}}{lim}\frac{\cos x-\sin x}{(\frac{\pi }{4}-x)(\cos x+\sin x)}$
$=\underset{x\to \frac{\pi }{4}}{lim}\frac{1-\tan x}{(\frac{\pi }{4}-x)(1+\tan x)}$.................(dividing the num and deno by cosx)
$=\underset{x\to \frac{\pi }{4}}{lim}\frac{\tan (\frac{\pi }{4}-x)}{(\frac{\pi }{4}-x)}=\underset{h\to 0}{lim}\frac{\tan h}{h}=1$