Question

Lim
x-0
l-Cos2x % 2 x²Cos²x ​

Answer 1

$\lim _{x \rightarrow0} [\frac{1 - \cos2x }{2 {x}^{2} \cos^{2} x } ]$

$\implies \lim _{x \rightarrow0} [\frac{2 \sin^{2}x }{2 {x}^{2} \cos^{2} x } ]$

$\implies \lim _{x \rightarrow0} [\frac{ \tan ^{2} x }{{x}^{2} } ]$

$\implies \lim _{x \rightarrow0} [\frac{ \tan x }{{x} } ] ^{2}$

$\sf \purple{ since : }$

$\red{ \boxed{\lim _{x \rightarrow0} \frac{ \tan x }{{x} } = 1}}$

$\implies {1}^{2}$

$\orange{ \therefore \: 1}$