Which of the following is equivalent to (√csc^2 x-1) / (√sec^2 x -1)? MULTIPLE CHOICE

Which of the following is equivalent to (√csc^2 x-1) / (√sec^2 x -1)? MULTIPLE CHOICE?
a) tan^4 x
b)cot^4 x
c)2_cotx
d)tan^7 xn

Work it out by using basic trigonometric properties and identities:

csc(x) = 1 / sin(x)
sec(x) = 1 / cos(x)

sin(x)^2 + cos(x)^2 = 1


csc(x)^2 - 1 =>
1/sin(x)^2 - 1 =>
(1 - sin(x)^2) / sin(x)^2 =>
cos(x)^2 / sin(x)^2 =>
cot(x)^2

sec(x)^2 - 1 =>
1/cos(x)^2 - 1 =>
(1 - cos(x)^2) / cos(x)^2 =>
sin(x)^2 / cos(x)^2 =>
tan(x)^2

sqrt(cot(x)^2) / sqrt(tan(x)^2) =>
cot(x) / tan(x) =>
cot(x) / (1/cot(x)) =>
cot(x)^2

EDIT:

Once again Brian, you and I get the same answer for the same question (I just got it before you...again), and once again I get a mysterious down-vote, even though my answer is correct. There's that coincidence again.

It's funny how you have to jump through hoops to get your answers all of the time.

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So Brian, why are you such a d*ck to everyone ??? I can understand that you like math but duh so do other people

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Brian has no work ethic because he always TD right answer(s) before his.

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Note that, by the Pythagorean Identities:
(a) csc^2(x) - 1 = cot^2(x)
(b) sec^2(x) - 1 = tan^2(x).

Therefore:
√[csc^2(x) - 1]/√[sec^2(x) - 1]
= √[cot^2(x)]/√[tan^2(x)], from above
= cot(x)/tan(x)
= cot(x)/[1/cot(x)], since tan(x) = 1/cot(x)
= cot^2(x).

I hope this helps!