Question

Solve:
$\cot {405}^o.\tan (-{495}^o)-\tan {585}^o.\cot (-{495}^o)=0$.

Answer 1

$\begin{array}{c}\cot {405}^0\cdot \tan \left(-{495}^0\right)-\tan {585}^0\cdot \cot \left(-{495}^0\right)=0\\ \Rightarrow -\left\{\cot \left(3\pi +\frac{\pi }{4}\right)\cdot \tan \left(3\pi -\frac{\pi }{4}\right)\right\}+\tan \left(3\pi +\frac{\pi }{4}\right)\cdot \cot \left(3\pi -\frac{\pi }{4}\right)\\ \Rightarrow -\left\{\cot \frac{\pi }{4}\cdot -\tan \frac{\pi }{4}\right\}+\left\{\tan \frac{\pi }{4}\cdot -\cot \frac{\pi }{4}\right\}\\ \left[\begin{array}{c}{405}^0=\left(2\pi +\pi /4\right)\\ {495}^0=3\pi -\pi /4\\ {585}^0=3\pi +\pi /4\end{array}\right]\\ \left(1-1\right)=0Ans.\end{array}$