Question

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

Answer 1

Clearly form of the limit is $\frac{0}{0}$
Thus applying L -Hospital's rule,
$\underset{x\to \pi /4}{lim}\frac{1-\tan x}{1-\sqrt{2}\sin x}=\underset{x\to \pi /4}{lim}\frac{-{\sec }^{2}x}{-\sqrt{2}\cos x}=2$