Which of the following is correct?

A. $$\mathop {\lim }\limits_{{\text{x}} \to 0} \left( {\frac{{\sin \,4{\text{x}}}}{{\sin \,2{\text{x}}}}} \right) = 1{\text{ and }}\mathop {\lim }\limits_{{\text{x}} \to 0} \left( {\frac{{\tan {\text{x}}}}{{\text{x}}}} \right) = 1$$

B. $$\mathop {\lim }\limits_{{\text{x}} \to 0} \left( {\frac{{\sin \,4{\text{x}}}}{{\sin \,2{\text{x}}}}} \right) = \infty {\text{ and }}\mathop {\lim }\limits_{{\text{x}} \to 0} \left( {\frac{{\tan {\text{x}}}}{{\text{x}}}} \right) = 1$$

C. $$\mathop {\lim }\limits_{{\text{x}} \to 0} \left( {\frac{{\sin \,4{\text{x}}}}{{\sin \,2{\text{x}}}}} \right) = 2{\text{ and }}\mathop {\lim }\limits_{{\text{x}} \to 0} \left( {\frac{{\tan {\text{x}}}}{{\text{x}}}} \right) = \infty $$

D. $$\mathop {\lim }\limits_{{\text{x}} \to 0} \left( {\frac{{\sin \,4{\text{x}}}}{{\sin \,2{\text{x}}}}} \right) = 2{\text{ and }}\mathop {\lim }\limits_{{\text{x}} \to 0} \left( {\frac{{\tan {\text{x}}}}{{\text{x}}}} \right) = 1$$

Answer: Option D