ImDaStyle

10+ Year Member
May 15, 2008
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Florida
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Pre-Pharmacy
This one problem is driving me insane, please help... =D

Verify!
cot^3x
-------- = cosx (csc^2x-1)
cscx
 

bigstix808

Mac Daddy Member
10+ Year Member
Oct 10, 2007
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GA
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Dentist
 

Streetwolf

Ultra Senior Member
10+ Year Member
7+ Year Member
Oct 25, 2006
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NJ
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Dentist
This one problem is driving me insane, please help... =D

Verify!
cot^3x
-------- = cosx (csc^2x-1)
cscx
cot(x) = cos(x)/sin(x)

csc(x) = 1/sin(x)

So [cos^3(x) / sin^3(x)] / (1/sin(x)) = cos^3(x) / sin^2(x)

cos^3(x) = cos(x)cos^2(x) = cos(x)*[1-sin^2(x)] = cos(x) - cos(x)sin^2(x)

Divide all that by sin^2(x) and you get cos(x)/sin^2(x) - cos(x).

That is the same as cos(x) * [1/sin^2(x) - 1].

That is the same as cos(x) * [csc^2(x) - 1].