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  1. #1
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    tan

    Hi all,

    I was wondering if i could get this confirmed...

    does arctan(x + tan(5*pi)) = arctan(x) + 5*pi?????

    Thanks in advance,
    ArTiCk
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  2. #2
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    Quote Originally Posted by ArTiCK View Post
    Hi all,

    I was wondering if i could get this confirmed...

    does arctan(x + tan(5*pi)) = arctan(x) + 5*pi?????

    Thanks in advance,
    ArTiCk
    Clearly not. Since tan(5 pi) = 0 the left hand side is just arctan x .....
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by ArTiCK View Post
    Hi all,

    I was wondering if i could get this confirmed...

    does arctan(x + tan(5*pi)) = arctan(x) + 5*pi?????

    Thanks in advance,
    ArTiCk
    Not in general, no. The inverse tangent function is not linear. That is to say defining f(x) = atn(x) then
    f(x + y) = f(x) + f(y)
    is not true for all x and y.

    -Dan
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  4. #4
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    I don't see why it would, because tan(5pi) is also tan(0), tan(pi), tan(2pi)... etc.
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  5. #5
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by ArTiCK View Post
    Hi all,

    I was wondering if i could get this confirmed...

    does arctan(x + tan(5*pi)) = arctan(x) + 5*pi?????

    Thanks in advance,
    ArTiCk
    IT can be clearly seen that this is untrue by looking at the integral case of each

    \arctan(x+5\pi)=\int\frac{dx}{1+(5\pi+{x})^2}dx


    and the other given by

    \arctan(x)+5\pi=\int\frac{dx}{1+x^2}+5\pi


    From there I think it can become obvious
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