Question

${lim}_{x\to o}\frac{4si{n}^{2\left(x{/}_2\right)co{s}^2\left(x{/}_2\right)}}{si{n}^2\left(x{/}_2\right)}=K$

Answer 1

We have,

${lim}_{x\to 0}\frac{4{\sin }^2\frac{x}{2}{\cos }^2\frac{x}{2}}{{\sin }^2\frac{x}{2}}=k$

Then,

${lim}_{x\to 0}4{\cos }^2\frac{x}{2}=k$

Taking limit and we get,

$k=4$

Hence, this is the answer.