Question

Evaluate:$\tan {495}^{\circ }-\cot {495}^{\circ }$

Answer 1

$\tan {495}^{\circ }-\cot {495}^{\circ }$

$=\tan {495}^{\circ }-\cot {495}^{\circ }$

$=\tan (5\times {90}^{\circ }+{45}^{\circ })-\cot (5\times {90}^{\circ }+{45}^{\circ })$

Here $n=5$ is odd , so $\tan$ changes to $\cot$ and $\cot$ changes to $\tan$

$=-\cot {45}^{\circ }-(-\tan {45}^{\circ })$ since ${495}^{\circ }=5\times {90}^{\circ }+{45}^{\circ }$ is in second quadrant,hence $\tan {495}^{\circ }$ is negative.

$=-1+1=0$