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Math Help - Help with trig identity proofs

  1. #1
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    Help with trig identity proofs

    Hi,
    I'm looking for help with two trig proof/verify problems. They are:


    1. SINX + COSX . COTX = CSCX


    2. ((1 + COSX) / SINX) + (SINX/ (1 + COSX)) = 2CSCX

    Thanks in Advance,
    Mike Clemmons
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  2. #2
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    Quote Originally Posted by Mike Clemmons View Post
    Hi,
    I'm looking for help with two trig proof/verify problems. They are:


    1. SINX + COSX . COTX = CSCX


    2. ((1 + COSX) / SINX) + (SINX/ (1 + COSX)) = 2CSCX

    Thanks in Advance,
    Mike Clemmons
    1. \sin{x} + \cos{x}\cot{x} = \sin{x} + \cos{x}\left(\frac{\cos{x}}{\sin{x}}\right)

     = \frac{\sin^2{x}}{\sin{x}} + \frac{\cos^2{x}}{\sin{x}}

     = \frac{\sin^2{x} + \cos^2{x}}{\sin{x}}

     = \frac{1}{\sin{x}}

     = \csc{x}.
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  3. #3
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    Quote Originally Posted by Mike Clemmons View Post
    Hi,
    I'm looking for help with two trig proof/verify problems. They are:


    1. SINX + COSX . COTX = CSCX


    2. ((1 + COSX) / SINX) + (SINX/ (1 + COSX)) = 2CSCX

    Thanks in Advance,
    Mike Clemmons
    2. \frac{1 + \cos{x}}{\sin{x}} + \frac{\sin{x}}{1 + \cos{x}}

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

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

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

     = \frac{1 + 2\cos{x} + 1}{\sin{x}(1 + \cos{x})}

     = \frac{2 + 2\cos{x}}{\sin{x}(1 + \cos{x})}

     = \frac{2(1 + \cos{x})}{\sin{x}(1 + \cos{x})}

     = \frac{2}{\sin{x}}

     = 2\csc{x}.
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    Prove it,
    Thanks very much..... On a different tack, we live in North Carolina, but lived in Manly NSW for about 3 years in the 80s. Loved every minute of it.
    Mike Clemmons
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  5. #5
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    Quote Originally Posted by Mike Clemmons View Post
    Prove it,
    Thanks very much..... On a different tack, we live in North Carolina, but lived in Manly NSW for about 3 years in the 80s. Loved every minute of it.
    Mike Clemmons
    I enjoyed Manly when I went there a few years ago. Awesome beach!
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