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Math Help - Cute trigo problem.

  1. #1
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    Cute trigo problem.

    sec(x)+tan(x)=t

    tan(x)=?(in form of t)
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    Re: Cute trigo problem.

    Quote Originally Posted by AaPa View Post
    sec(x)+tan(x)=t

    tan(x)=?(in form of t)
    A quick rundown...As typical with me this is a rather "brute force" approach. I'll leave the details to the reader.

    First put the equation into sines and cosines. Then solve for sin(x):
    sin(x) = t~cos(x) - 1
    Hold on to this equation.

    Now square both sides and use cos^2(x) = 1 - sin^2(x) to put the equation in terms of only cosine. You can factor out a cos(x) from each side. Then solve for cos(x) getting:
    cos(x) = \frac{2t}{t^2 + 1}

    Now put this expression for cos(x) into the above sin(x) equation. Then
    tan(x) = \frac{sin(x)}{cos(x)} = \frac{t}{2} - \frac{1}{2t}

    Notice that this equation does not have the same domain as the original equation. I'll leave the details of that to you as well.

    -Dan
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  3. #3
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    Re: Cute trigo problem.

    Hello, AaPa!

    \sec x+\tan x \:=\:t

    \text{Write }\tan x\text{ in terms of }t.

    We have:. \sec x \;=\;t - \tan x

    Square: . \sec^2\!x \;=\;t^2 - 2t\tan x + \tan^2\!x

    . . . . \tan^2\!x+1 \;=\;t^2-2t\tan x + \tan^2\!x

    n . . . . 2t\tan x \;=\;t^2-1

    . . . . . . . \tan x \;=\;\frac{t^2-1}{2t}
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  4. #4
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    Re: Cute trigo problem.

    yes right. i used the second method.
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