Question

If $\frac{\sin A}{\sin B}=\frac{\sqrt{3}}{2}$ and $\frac{\cos A}{\cos B}=\frac{\sqrt{5}}{2},0<A,B<\pi /2$, then $\frac{\tan A}{\tan B}$ is equal to.

• A. $\frac{\sqrt{3}}{\sqrt{5}}$
• B. $\frac{\sqrt{5}}{\sqrt{3}}$
• C. $1$
• D. $\frac{(\sqrt{5}+\sqrt{3})}{\sqrt{5}}$

Answer 1

The correct option is A $\frac{\sqrt{3}}{\sqrt{5}}$

$\frac{\tan A}{\tan B}=\frac{\frac{\sin A}{\cos A}}{\frac{\sin B}{\cos B}}=\frac{\sin A}{\sin B}\times \frac{\cos B}{\cos A}=\frac{\sqrt{3}}{2}\times \frac{2}{\sqrt{5}}=\frac{\sqrt{3}}{\sqrt{5}}$

Therefore, Answer is $\frac{\sqrt{3}}{\sqrt{5}}$