Question

Solve:
$\underset{x\to \pi /4}{lim}\frac{1-\tan x}{1-\sqrt{2}\sin x}$

Answer 1

We have,

${lim}_{x\to \frac{\pi }{4}}\frac{1-\tan x}{1-\sqrt{2}\sin x}$

$UsingL-Hospitalrule{lim}_{x\to \frac{\pi }{4}}\frac{-{\sec }^{2}x}{-\sqrt{2}\cos x}{lim}_{x\to \frac{\pi }{4}}\frac{{\sec }^{3}x}{\sqrt{2}}$

$=\frac{(\sqrt{2}{)}^3}{\sqrt{2}}$

$=2$

Hence, this is the answer.