Question

Tan(-x)csc(-x)/sec(-x)cot(-x) simplify the expression

Answer 1

$\bf \cfrac{tan(-x)csc(-x)}{sec(-x)cot(-x)}\implies \cfrac{\quad \frac{sin(-x)}{cos(-x)}\cdot \frac{1}{sin(-x)}\quad }{\frac{1}{cos(-x)}\cdot \frac{cos(-x)}{sin(-x)}}\implies \cfrac{\quad \frac{1}{cos(-x)}\quad }{\frac{1}{sin(-x)}} \\\\\\ \cfrac{1}{cos(-x)}\cdot \cfrac{sin(-x)}{1}\implies \cfrac{sin(-x)}{cos(-x)}\implies \cfrac{\stackrel{\stackrel{symmetry}{identities}}{-sin(x)}}{cos(x)}\implies -tan(x)$