Question

find the value of k,if $f\left(x\right)=\{{}_{\text{k},\text{x}=0}^{\frac{1-\cos 2x}{1+\cos 2x},x\ne 0}$ is continuous at $x=0$.

Answer 1

As $f\left(x\right)$ is continuous at $x=0$, $\underset{x\to 0}{lim}f\left(x\right)=k$

$\underset{x\to 0}{lim}\frac{1-\cos 2x}{1+\cos 2x}=k$

$\frac{1-1}{1+1}=k⟹k=0$