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Math Help - Simplifying Trig Functions

  1. #1
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    Simplifying Trig Functions

    1)I'm supposed to simplify:

    Sin ( ArcCot (Sec (ArcTan (x) ) ) )

    It's been a while since I've had to do these and I can't remember how to start.

    2) Show that ArcSin ((x-1)/(x+1)) = 2 ArcTan (x^(1/2) - pi/2)

    I have no clue on this one...

    Any thoughts?

    Not looking for answers per say, but ideas on what direction to take...
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  2. #2
    Member Abu-Khalil's Avatar
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    Draw a triangle rectangle which sides are x,1 and \sqrt{x^2+1} so \text{arcsec} \frac{\sqrt{x^2+1}}{x} =\theta=\arctan x, etc.
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  3. #3
    MHF Contributor matheagle's Avatar
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    Quote Originally Posted by TyrsFromAbove37 View Post
    1)I'm supposed to simplify:

    Sin ( ArcCot (Sec (ArcTan (x) ) ) )

    It's been a while since I've had to do these and I can't remember how to start.

    2) Show that ArcSin ((x-1)/(x+1)) = 2 ArcTan (x^(1/2) - pi/2)

    I have no clue on this one...

    Any thoughts?

    Not looking for answers per say, but ideas on what direction to take...

    Make a substitution. Let u= what's inside. So in (1), let
    u=\arctan x. From that you have a triangle
    since this means that \tan u=x/1. So, u is an angle in your right triangle, and not the right angle, tangent is opposite over hippopotamus. So draw it with x as the length of the opposite side and 1 as your hippo.
    Figure out that other side by a^2+b^2=c^2. Then get sec U....
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