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)#