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Math Help - Trig Identities - Simplifying

  1. #1
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    Trig Identities - Simplifying

    (Cot^2 X)/(1+ Csc X) + Sin X * Csc X

    It's been a while on this stuff, but what does this simplify down to?
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  2. #2
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    Quote Originally Posted by gregmosu View Post
    (Cot^2 X)/(1+ Csc X) + Sin X * Csc X

    It's been a while on this stuff, but what does this simplify down to?
    Change everything to sin and cos

    Spoiler:
    \frac{\cos ^2 x}{\sin ^2 x (1+ \frac{1}{\sin x})}+1

    1+\frac{1}{\sin(x)} = \frac{\sin (x) + 1}{\sin(x)}


    \frac{\cos ^2 x}{\sin  x+ \sin ^2x}+1 = \frac{\cos^2 x + \sin x + \sin ^2x}{\sin x + \sin ^2 x} = \frac{\sin x}{\sin x(1+\sin x)}
     \frac{1}{1+\sin x}
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  3. #3
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    Quote Originally Posted by gregmosu View Post
    (Cot^2 X)/(1+ Csc X) + Sin X * Csc X

    It's been a while on this stuff, but what does this simplify down to?
    Can you show us your work so far, then we can help where you get stuck.
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  4. #4
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    Here's my work one step at a time.

    1) (Cot^2 X)/(1 + Csc X) + (1/Csc X) * Csc X

    2) (Cot^2 X)/(1 + Csc X) + 1

    3) (Csc^2 X - 1)/(1 + Csc X) + 1


    Is this right so far?

    Actually after taking a second look, it appears that this would simplify to Csc X.
    Last edited by gregmosu; April 13th 2010 at 08:26 AM.
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  5. #5
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    Quote Originally Posted by gregmosu View Post
    Here's my work one step at a time.

    1) (Cot^2 X)/(1 + Csc X) + (1/Csc X) * Csc X

    2) (Cot^2 X)/(1 + Csc X) + 1

    3) (Csc^2 X - 1)/(1 + Csc X) + 1


    Is this right so far?
    Yes, that's fine.

    Next -- use the difference of two squares on  \csc ^2(x) - 1

    edit: you'd be right -- it does equal csc(x)
    Last edited by e^(i*pi); April 14th 2010 at 07:35 AM.
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