Question

Find the value of $\cos (\frac{3\pi }{2}+n)\cos (2\pi +n)[\cot (\frac{3\pi }{2}-n)+\cot (2\pi +n)]$

Answer 1

Given expression can be rewritten as

$\Rightarrow \sin \left(n\right)\cos \left(n\right)[\tan \left(n\right)+\cot n]$

$\Rightarrow \sin n\cos n[\frac{\sin n}{\cos n}+\frac{\cos n}{\sin n}]$

$\Rightarrow \sin n\cos n\left[\frac{{\sin }^{2}n+{\cos }^{2}n}{\sin n\cos n}\right]$

$\Rightarrow [{\sin }^{2}n+{\cos }^{2}n]$

$=+1$