Question

The value of $\frac{\left(\cos {11}^{\circ }+\sin {11}^{\circ }\right)}{\left(\cos {11}^{\circ }-\sin {11}^{\circ }\right)}$ is

• A. $\tan {304}^{\circ }$
• B. $\tan {56}^{\circ }$
• C. $\cot {11}^{\circ }$
• D. $\tan {34}^{\circ }$

Answer 1

The correct option is B $\tan {56}^{\circ }$

$\frac{\cos {11}^{\circ }+\sin {11}^{\circ }}{\cos {11}^{\circ }-\sin {11}^{\circ }}=\frac{1+\tan {11}^{\circ }}{1-\tan {11}^{\circ }}=\frac{\tan {45}^{\circ }+\tan {11}^{\circ }}{1-\tan {45}^{\circ }\tan {11}^{\circ }}=\tan ({45}^{\circ }+{11}^{\circ })=\tan {56}^{\circ }$