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Math Help - trig identity question

  1. #1
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    trig identity question

    if
    sec^2 x - tan^2 x =1

    is sec^4 x - tan^4 x =1 or any other bigger even power will also be like this?
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  2. #2
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    Re: trig identity question

    Quote Originally Posted by ameerulislam View Post
    if
    sec^2 x - tan^2 x =1

    is sec^4 x - tan^4 x =1 or any other bigger even power will also be like this?
    NO!


    That is true because $\tan^2(x)=\sec^2(x)-1$.
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  3. #3
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    Re: trig identity question

    Quote Originally Posted by Plato View Post
    NO!


    That is true because $\tan^2(x)=\sec^2(x)-1$.
    ok, so is there any work around like $(\tan^2(x))^2=(\sec^2(x))^2-1$
    sorry if I sound stupid..
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  4. #4
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    Re: trig identity question

    my original problem was $\int \frac{(3x^3)}{\sqrt {x^2-25}} dx$

    used trig substitution technique to substitute $x, x=a sec^2x$
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  5. #5
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    Re: trig identity question

    Quote Originally Posted by ameerulislam View Post
    my original problem was $\int \frac{(3x^3)}{\sqrt {x^2-25}} dx$

    used trig substitution technique to substitute $x, x=a sec^2x$
    Use $x=5 sec(u)$ then $dx=5\tan(u)\sec(u)du$

    Notice that $\sqrt{25\sec^2(u)-25}=5\sqrt{\sec^2(u)-1}$

    This should a lesson: Post the actual question first.
    Last edited by Plato; March 8th 2014 at 11:16 AM.
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