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Math Help - identity?

  1. #1
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    identity?

    Find an exact solution to the equation below so that 0 < x< pi

    (1+tan(x)) / sin(x) = 0
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  2. #2
    Senior Member pacman's Avatar
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    ah, you mean trigonometric equation?

    (1+tan(x)) / sin(x) = 0.

    cross multiplying, 1 + tan x = 0

    tan x = -1

    x = arctan (-1)

    x = -45 degrees = pi/4 radians

    or if u want a family of solutions, x = (pi/4)(4k - 1), where k is an element of Z.

    look at the graph
    Attached Thumbnails Attached Thumbnails identity?-tangent.gif  
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  3. #3
    Senior Member pacman's Avatar
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    But what if (1 + tan x)/sin x = 0 is written this way,

    surely sin x is included,

    (1 + tan x)/sin x = (1 + tan x)(csc x) = 0, simplifying

    csc x + sec x = 0,

    csc x = - sec x

    1/sin x = - 1/ cos x

    sin x/cos x = tan x = -1, same as above.

    but i really wonder why the graph of csc x + sec x behave differently,

    see below,
    Attached Thumbnails Attached Thumbnails identity?-secant-cosecant.gif  
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