$\lim _{x ightarrow 0} \frac{(1-\cos 2 x)(3+\cos x)}{x an 4 x}$ has the value

Question

$\lim _{x ightarrow 0} \frac{(1-\cos 2 x)(3+\cos x)}{x 	an 4 x}$ has the value

Aicharya · Accepted Answer

$\begin{aligned} & \lim _{x ightarrow 0} \frac{(1-\cos 2 x)(3+\cos x)}{x 	an 4 x} \ & =\lim _{x ightarrow 0} \frac{2\left(\frac{\sin ^2 x}{x^2}ight) 	imes(3+\cos x)}{4\left(\frac{	an 4 x}{4 x}ight)} \ & =\frac{2(1)^2 	imes(3+1)}{4}=2\end{aligned}$

$\lim _{x \rightarrow 0} \frac{(1-\cos 2 x)(3+\cos x)}{x \tan 4 x}$ has the value

Solution