## Trig integral help

Limits, differentiation, related rates, integration, trig integrals, etc.
Andromeda
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Joined: Tue Oct 12, 2010 1:56 am
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### Trig integral help

I am having difficulty finding integral((tanx)^2 / (secx)^2)dx.

I tried converting everything in terms of sinx and cosx but that doesn't seem to help.

stapel_eliz
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Andromeda wrote:I am having difficulty finding integral((tanx)^2 / (secx)^2)dx.

I tried converting everything in terms of sinx and cosx but that doesn't seem to help.

Once you've simplified and gotten an expression in just sine, you can use the double-angle formula (in reverse) for the cosine:

. . . . .$\sin^2(x)\, =\, \frac{1}{2}\left(1\, -\, \cos(2x\right)$

Then the integral is pretty straightforward.

Note: You will be using the double-angle formulas (in reverse) a lot in calculus, so make sure you're solid on them!

Andromeda
Posts: 11
Joined: Tue Oct 12, 2010 1:56 am
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### Re:

stapel_eliz wrote:
Andromeda wrote:I am having difficulty finding integral((tanx)^2 / (secx)^2)dx.

I tried converting everything in terms of sinx and cosx but that doesn't seem to help.

Once you've simplified and gotten an expression in just sine, you can use the double-angle formula (in reverse) for the cosine:

. . . . .$\sin^2(x)\, =\, \frac{1}{2}\left(1\, -\, \cos(2x\right)$

Then the integral is pretty straightforward.

Note: You will be using the double-angle formulas (in reverse) a lot in calculus, so make sure you're solid on them!

I'm still not sure I understand. Once I convert this into terms of sinx and cosx I have integral((sinx)^2 / (cosx)^4)dx. After that I should use the double angle forumual or half angle? The one you showed me is the half angle formual.

snowdrifter
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Joined: Tue Jan 11, 2011 4:52 pm
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### Re: Trig integral help

It simplifies like this:

(tanx)/(secx)
= ((sinx/cosx)/(1/(cosx))
=((sinx/cosx)*((cosx))
=sinx

It works the same way for the squared functions.