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Thread: trig identities that add years to your life

  1. #1
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    trig identities that add years to your life

    Hi folks,

    Given $y = e^x \tan x$ we have to show that $\dfrac{d^2 y}{dx^2} = e^x (2 \tan^3 x + 2 \tan^2 x + 3 \tan x + 2)$

    now I get $\dfrac{d^2 y}{dx^2} = e^x (2 \sec^2 x \tan x + 2 \sec^2 x + \tan x)$

    so somehow $2 \sec^2 x \tan x + 2 \sec^2 x + \tan x = 2 \tan^3 x + 2 \tan^2 x + 3 \tan x + 2$

    I have been horsing around for ages not getting there. A hint would be nice, lest I die of old age.

    Thanks
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  2. #2
    Forum Admin topsquark's Avatar
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    Re: trig identities that add years to your life

    Quote Originally Posted by s_ingram View Post
    Hi folks,

    Given $y = e^x \tan x$ we have to show that $\dfrac{d^2 y}{dx^2} = e^x (2 \tan^3 x + 2 \tan^2 x + 3 \tan x + 2)$

    now I get $\dfrac{d^2 y}{dx^2} = e^x (2 \sec^2 x \tan x + 2 \sec^2 x + \tan x)$

    so somehow $2 \sec^2 x \tan x + 2 \sec^2 x + \tan x = 2 \tan^3 x + 2 \tan^2 x + 3 \tan x + 2$

    I have been horsing around for ages not getting there. A hint would be nice, lest I die of old age.

    Thanks
    Hint: $\displaystyle tan^2 (x) + 1 = sec^2(x)$

    -Dan
    Last edited by topsquark; Apr 15th 2018 at 10:54 AM.
    Thanks from s_ingram
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  3. #3
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    Re: trig identities that add years to your life

    Have you thought about the alternative to "dying of old age"?
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    Re: trig identities that add years to your life

    "Lest I die of old age ..... without getting an answer!" was what I meant, but you are right. I didn't say what I meant.
    With Dan's hint it came out in a few seconds.
    The only alternative I can think of to dying of old age, is to die young!
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  5. #5
    Forum Admin topsquark's Avatar
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    Re: trig identities that add years to your life

    Quote Originally Posted by s_ingram View Post
    "Lest I die of old age ..... without getting an answer!" was what I meant, but you are right. I didn't say what I meant.
    With Dan's hint it came out in a few seconds.
    The only alternative I can think of to dying of old age, is to die young!
    To quote the immortal Billy Joel: Only the good die young.

    I'm going to live forever.

    -Dan
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