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Math Help - Some analytic trig questions

  1. #1
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    Some analytic trig questions

    first is 1+tan^2x/csc^2x.. I get it down to 1/cos^2x* sin^2x/1. Answer is supposed to be tan^2(x)

    also
    (sec^2x+csc^2x)-(tan^2x+cot^2x)
    I got this down to
    (1/cos^2*sin^2x)-(tan^2x*tan^2x+1/tan^2x)
    answer books says it all equals 2

    Please show me how to do these problems. Thanks in advance.
    Last edited by bilbobaggins; March 4th 2008 at 03:47 PM.
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  2. #2
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    Quote Originally Posted by bilbobaggins View Post
    first is 1+tan^2x/csc^2x.. I get it down to 1/cos^2x* sin^2x/1. Answer is supposed to be tan^2(x)
    (sigh) Please use parenthesis. You meant (1 + tan^2(x))/csc^2(x).

    \frac{1 + tan^2(x)}{csc^2(x)} = \frac{sec^2(x)}{csc^2(x)}

    Can you continue?

    -Dan
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  3. #3
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    Quote Originally Posted by bilbobaggins View Post
    first is 1+tan^2x/csc^2x.. I get it down to 1/cos^2x* sin^2x/1. Answer is supposed to be tan^2(x)

    also
    (sec^2x+csc^2x)-(tan^2x+cot^2x)
    I got this down to
    (1/cos^2*sin^2x)-(tan^2x*tan^2x+1/tan^2x)
    answer books says it all equals 2

    Please show me how to do these problems. Thanks in advance.
    tan^2(x) + 1 = sec^2(x)

    and there is a similar relation for the csc and cot functions.

    -Dan
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  4. #4
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    Hello, Bilbo!

    First is:. \frac{1+\tan^2\!x}{\csc^2\!x}
    I get it down to:. \frac{1}{\cos^2\!x}\cdot\frac{\sin^2\!x}{1}

    Answer is supposed to be: . \tan^2\!x

    You have: . \frac{\sin^2\!x}{\cos^2\!x}\;=\;\left(\frac{\sin x}{\cos x}\right)^2 . . . Got it?




    (\sec^2\!x+\csc^2\!x)-(\tan^2\!x+\cot^2\!x)

    Book says it all equals 2.

    \text{We have: }\;\underbrace{(\sec^2\!x-\tan^2\!x)}_{\text{This is 1}} + \underbrace{(\csc^2\!x - \cot^2\!x)}_{\text{This is 1}} . . . Okay?

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  5. #5
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    Quote Originally Posted by Soroban View Post
    Hello, Bilbo!


    You have: . \frac{\sin^2\!x}{\cos^2\!x}\;=\;\left(\frac{\sin x}{\cos x}\right)^2 . . . Got it?





    \text{We have: }\;\underbrace{(\sec^2\!x-\tan^2\!x)}_{\text{This is 1}} + \underbrace{(\csc^2\!x - \cot^2\!x)}_{\text{This is 1}} . . . Okay?

    What did you do for the second one?
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