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Please help me! I have no idea how to do this and any hints you could give me would be great! THANKS GUYS!!! :)

2006-10-19 14:30:44 · 1 answers · asked by cheezo12 1 in Science & Mathematics Mathematics

1 answers

First, we note that:

d(csc x)/dx = -cos x/sin² x = -cot x csc x
d(cot x)/dx = (-sin² x - cos² x)/sin² x = -csc² x

By the chain rule:

d(ln (csc x-cot x))/dx = (-cot x csc x + csc² x)/(csc x - cot x)

We cancel out the csc x:

(-cot x + csc x)/(1-cos x)

factor the numerator:

(csc x)(-cos x + 1)/(1-cos x)

Canceling the 1-cos x:

csc x

So d(ln (csc x-cot x))/dx = csc x. Integrating both sides then gives us:

ln (csc x-cot x) + C = ∫csc x dx

Which was to be demonstrated.

2006-10-19 15:28:24 · answer #1 · answered by Pascal 7 · 0 0

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