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Math Help - Trig Properties - Due tomorrow morning!

  1. #1
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    Trig Properties - Due tomorrow morning!

    Hi, I just got slipped up on a few problems here, not sure which angle to attack from all thetas will be x, since i am ignorant about symbols, etc

    Simplify
    1. (2sinxcosx + 2cosx)/(cosx((sin^2)x - 1))

    2. (tanx + tanxsinx - cosxsinx)/(sinxtanx)

    3. [(coxtanx)/tan(90degrees - x)] - 1/(sin(90degrees - x))

    4. [(2 + (tan^2)x)/(sec^2)x] - 1

    Any help is much appreciated
    Thanks so much
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  2. #2
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    Here is the first one.
    Attached Thumbnails Attached Thumbnails Trig Properties - Due tomorrow morning!-picture6.gif  
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  3. #3
    MHF Contributor
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    Quote Originally Posted by ThePerfectHacker View Post
    Here is the first one.
    PerfectHacker's solution made the original more complex.

    Here is one way.

    (2sinxcosx + 2cosx)/(cosx((sin^2)x - 1))

    = 2cosX(sinX +1) / cosX(sin^2(X) -1)
    The cosX cancels out,
    = 2(sinX +1) / (sinX +1)(sinX -1)
    The (sinX +1) cancels out,
    = 2 / (sinX -1) -----------------------answer.
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  4. #4
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    Hello, leviathanwave!

    Code:
        tan(x) + tan(x)·sin(x) - cos(x)·sin(x)
    2. ---------------------------------------
                      sin(x)·tan(x)

    Multiply top and bottom by cos(x):
    Code:
      sin(x) + sinē(x) - sin(x)·cosē(x)
      ---------------------------------
                   sinē(x)
    
        sin(x)·[1 + sin(x) - cosē(x)]
    =   -----------------------------
                   sinē(x)
    
        1 - cosē(x) + sin(x)
    =   --------------------
               sin(x)
    
         sinē(x) + sin(x)
    =   ------------------
              sin(x)
    
         sin(x)·[sin(x) + 1]
    =   --------------------
              sin(x)
    
    
    =   sin(x) + 1
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  5. #5
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    Hello again, leviathanwave!

    Code:
         2 + tanē(x) 
    4.  ------------ - 1
           secē(x)
    Code:
    1 + 1 + tanē(x)           1 + secē(x)
    --------------- - 1   =   ----------- - 1
         secē(x)                secē(x)
    
             1      secē(x)              1
      =   ------- + ------- - 1   =   ------- + 1 - 1
          secē(x)   secē(x)           secē(x)
    
             1
      =   -------   =   cosē(x)
          secē(x)
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