Question

The value of $\frac{\cos {15}^{\circ }+\sin {15}^{\circ }}{\cos {15}^{\circ }-\sin {15}^{\circ }}$ is

• A. $\frac{1}{\sqrt{3}}$
• B. $1$
• C. $\frac{1}{2}$
• D. $\sqrt{3}$

Answer 1

The correct option is D $\sqrt{3}$

$\frac{\cos {15}^{\circ }+\sin {15}^{\circ }}{\cos {15}^{\circ }-\sin {15}^{\circ }}=\frac{1+\frac{\sin 15°}{\cos 15°}}{1-\frac{\sin 15°}{\cos 15°}}=\frac{\tan 45°+\tan 15°}{1-\tan 45°\tan 15°}=\tan 60°=\sqrt{3}$