Question

Find the value of
$\cos {225}^{\circ }-\sin {225}^{\circ }+\tan {495}^{\circ }-\cot {495}^{\circ }$

Answer 1

$\begin{array}{c}\cos {225}^{\circ }-\sin {225}^{\circ }+\tan {495}^{\circ }-\cot {495}^{\circ }\\ =\cos \left(180+45\right)-\sin \left(180+45\right)+\tan \left(540-45\right)-\cot \left(540-45\right)\\ =-\cos 45+\sin 45+\tan \left(3\pi -45\right)-\cot \left(3\pi -45\right)\\ =-\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}-\tan 45+\cot 45\\ =-1+1=0\end{array}$