Question

Soluation :-
$\underset{x\to \frac{\pi }{4}}{lim}\left(\frac{1-\tan x}{1-\sqrt{2}\sin x}\right)$ is equal to.

• A. $0$
• B. $1$
• C. $-2$
• D. $2$

Answer 1

The correct option is D $2$

Solution -

${lim}_{x\to \frac{\pi }{4}}\frac{1-tanx}{1-\sqrt{2}sinx}$

Apply L-Hospital Rule -

${lim}_{x\to \frac{\pi }{4}}\frac{-tanxse{c}^{2}x}{-\sqrt{2}cosx}$

${lim}_{x\to \frac{\pi }{4}}\frac{tanxse{c}^{3}x}{\sqrt{2}}$

$=2$