How to get (secx)(tanx) from (1/cosx)(sinx/cosx)?

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SUMMARY

The discussion centers on the transformation of the function h(x) = sin(x)/cos²(x) into the product of sec(x) and tan(x). Participants clarify that sin(x)/cos²(x) simplifies to (1/cos(x))(sin(x)/cos(x)), which equals (sec(x))(tan(x)). The conversation also touches on finding the antiderivative of sec(x)tan(x), with suggestions to use substitution, specifically letting cos(x) = t. The final conclusion emphasizes the need for clarity in problem statements to facilitate understanding.

PREREQUISITES
  • Understanding of trigonometric identities, specifically secant and tangent functions.
  • Knowledge of derivatives and antiderivatives in calculus.
  • Familiarity with substitution methods for integration.
  • Basic algebraic manipulation of trigonometric functions.
NEXT STEPS
  • Learn how to find the antiderivative of sec(x)tan(x).
  • Study the method of substitution in integration.
  • Explore trigonometric identities and their applications in calculus.
  • Practice simplifying trigonometric expressions using identities.
USEFUL FOR

Students and educators in calculus, particularly those focusing on trigonometric functions and integration techniques. This discussion is beneficial for anyone looking to enhance their understanding of derivatives and antiderivatives involving trigonometric identities.

helpm3pl3ase
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Quick question:

h(x) = sinx/cos^(2) x

= (1/cosx)(sinx/cosx)

Then you get (secx)(tanx)..

I do not get how they get secx x tanx?? Anyone?? Thanks
 
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1/cos(x) is also called sec(x).

sin(x)/cos(x) is also called tan(x).

- Warren
 
so the answer would be

(secx)(tanx) + c

Correct??
 
All you've done so far is convert the function you gave me into a slightly simpler form.

sin(x) / cos^2(x) = sec(x) tan(x).

Since you didn't actually post the problem as it was given to you, I don't know if h(x) is a function of which you need to find the antiderivative, or whether you've already done that step. You probably need to actually perform the antiderivative now.

- Warren
 
sorry how would i go about doing this.. Iam so confused.
 
Find the function which has a derivative of sec(x) tan(x). You should have a list of such facts in your book.

- Warren
 
alright.. I get it now.. Sorry.. I don't know why this problem was causing me problems.. Thanks for clearing it up.
 
Do you know the method of substitution to find antiderivatives ? If so, just plug

\cos x = t

and c what u get.

Daniel.
 
It would have helped if you had told us from the beginning that you were trying to find an anti-derivative! All you said was that you couldn't see how they had gone from Quick question:

h(x) = sinx/cos^(2) x

to h(x)= (secx)(tanx).
 

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