MCQ
$\lim_{x \rightarrow 0} {{\left( \frac{1+\tan x}{1+\sin x} \right)}^{\cos ecx}}=.......$
- A$\frac{1}{e}$
- B$1$
- ✓$e$
- D${{e}^{2}}$
$\lim_{x \rightarrow 0} {{\left( \frac{1+\tan x}{1+\sin x} \right)}^{cosec x}}$
$=\lim_{x \rightarrow 0}\frac{\left(\left(1+\tan x\right)^\frac{1}{\tan x}\right)^{\sec x}}{\left(1+\sin x\right)^\frac{1}{\sin x}}$
$=\lim_{x \rightarrow 0}\frac{e^{\sec x}}{\left(1+\sin x\right)^\frac{1}{\sin x}}\Rightarrow \frac{e^{\sec 0}}{1}\Rightarrow e$
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