Question

$\frac{\cos {13}^{\circ }-\sin {13}^{\circ }}{\cos {13}^{\circ }+\sin {13}^{\circ }}-\frac{1}{\cot {180}^{\circ }}=$

• A. $\tan {77}^{\circ }$
• B. $\cot {77}^{\circ }$
• C. $\tan {32}^{\circ }$
• D. $0$

Answer 1

Answer: (C)

$\tan {32}^{\circ }$

$\frac{\cos {13}^{\circ }-\sin {13}^{\circ }}{\cos {13}^{\circ }+\sin {13}^{\circ }}+\frac{1}{\cot {180}^{\circ }}=\frac{1-\tan {13}^{\circ }}{1+\tan {13}^{\circ }}+\tan {180}^{\circ }\left[\text{Dividing the first term by}\cos {13}^{\circ }\right]=\frac{\tan {45}^{\circ }-\tan {13}^{\circ }}{1+\tan {45}^{\circ }\tan {13}^{\circ }}+0=\tan ({45}^{\circ }-{13}^{\circ })=\tan {32}^{\circ }$