Mathematics: Simplify the expression tan(-x)csc(-x)/sec(-x)cot(-x)

Simplify the expression tan(-x)csc(-x)/sec(-x)cot(-x)

Ответ:

kealalac1

01.01.2022

$\frac{ tan(-x) cosec (-x)}{sec (-x) cot (-x)}$ ≡ $\frac{ [- tan(x)] [-cosec (-x)]}{[sec (x)] [-cot (x)]}$

≡ $\frac{ tan(x) cosec (-x)}{-sec (x) cot (x)}$

≡ $\frac{ (\frac{sin (x)}{cos (x)}) (\frac{1}{sin (x )}) }{(- \frac{1}{cos (x)}) ( \frac{cos (x)}{sin (x)}) }$

≡ $\frac{ \frac{1}{cos (x)} }{- \frac{1}{sin (x)} }$

≡ $- \frac{sin (x)}{cos (x)}$

≡ - tan (x)