Question

The value of $\frac{\cos {11}^o+\sin {11}^o}{\cos {11}^o-\sin {11}^o}$ is-

• A. $\tan {56}^o$
• B. $\sin {56}^o$
• C. $\cos {56}^o$
• D. $\cot {56}^o$

Answer 1

The correct option is A $\tan {56}^o$

$\frac{\cos {11}^{\circ }+\sin {11}^{\circ }}{\cos {11}^{\circ }-\sin {11}^{\circ }}$

$=\frac{\cos {11}^{\circ }+\cos \left({90}^{\circ }-{11}^{\circ }\right)}{\cos {11}^{\circ }-\cos \left({90}^{\circ }-{11}^{\circ }\right)}$

$=\frac{\cos {11}^{\circ }+\cos {79}^{\circ }}{\cos {11}^{\circ }-\cos {79}^{\circ }}$

$=\frac{2\cos {45}^{\circ }\cos {34}^{\circ }}{2\sin {45}^{\circ }\cos {34}^{\circ }}$

$=\frac{\frac{2}{\sqrt{2}}\cos {34}^{\circ }}{\frac{2}{\sqrt{2}}\sin {34}^{\circ }}$

$=\cot {34}^{\circ }$

$=\tan ({90}^{\circ }-{34}^{\circ })$

$=\tan {56}^{\circ }$