How do you simplify $csc(-x)/cot(-x)$ ?

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Answer 1 · 2016-09-05T15:01:50

$csc(-x)/cot(-x)=-csc x/-cot x=(csc x)/(cot x)=(1/sinx)/(cos x/sin x)$

$=1/cos x=sec x$ .

Answer 2 · 2016-09-05T15:04:05

$sec(x)$

We have: $(csc(- x)) / (cot(- x))$

Let's apply the fact that $csc(x)$ and $cot(x)$ are odd functions:

$= (- csc(x)) / (- cot(x))$

$= (csc(x)) / (cot(x))$

Then, let's apply two standard trigonometric identities; $csc(x) = (1) / (sin(x))$ and $cot(x) = (cos(x)) / (sin(x))$ :

$= ((1) / (sin(x))) / ((cos(x)) / (sin(x)))$

$= (1) / (sin(x)) cdot (sin(x)) / (cos(x))$

$= (1) / (cos(x))$

Finally, let's apply another standard trigonometric identity; $sec(x) = (1) / (cos(x))$ :

$= sec(x)$

How do you simplify csc(-x)/cot(-x)csc(-x)/cot(-x)?