Question

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

Answer 1

${lim}_{x\to \frac{\pi }{4}}\frac{1-\tan x}{1-\sqrt{2}\sin x}\frac{0}{0}$ form

Using L-Hospital rule

${lim}_{x\to \frac{\pi }{4}}\frac{0-{\sec }^{2}x}{0-\sqrt{2}\cos x}=\frac{{\left(\sqrt{2}\right)}^2}{\sqrt{2}\times \frac{1}{\sqrt{2}}}=2$