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Need help with some identity problems

  1. Jun 29, 2008 #1
    I'm having difficulties with a few identity problems and I wanted to make sure I'm doing the ones I believe I did correctly, correctly...

    1. (cos^3x)+(sin^2x)(cosx)

    2. (1+cosy)/(1+secy)

    3. (tanx)/(secx)



    6. (1+sinx/cosx)+(cosx/1+sinx)

    7. (tanx)(cosx)(cscx)

    The ones that I'm not too sure about are 2 and 8. I feel pretty confident about the other ones, but I wanted to make sure I'm doing them correctly.

    Thanks a lot to anybody that helps.
  2. jcsd
  3. Jun 29, 2008 #2


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    Homework Helper

    For 2
    From the text in red, multiply both the numerator and denominator by cosy

    I don't see a question 8...the only one that looked wrong at a glance was 2.
  4. Jun 29, 2008 #3
    First, you did not put a #8 up so I guess you are confident about that one lol.

    I didn't look at #6 b/c my eyes are tired, but you will want to check 2 and 4!

    for #2 you have that 1+(1/cos(y)) = 1 + cos(y) !! since when is that true. instead, you should multiply the numerator and denominator by cos(y) then see what you get.

    #4 the hint is to look at what 1 - (cos(x))^2 is
  5. Jun 29, 2008 #4


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    Where did you get the "2"?

    (cosx)(cos^2x)+ (sin^2x)(cosx)= cos(x)(cos^2x+ sin^2x).

    How did you make this jump? 1/cosy is NOT equal to cos y.

    Yes, that's right.

    You've got your parenthes wrong. Also sec x= 1/cosx not 1/sin x
    (1/cosx- cosx)(cos(x)/sin(x)= (1/cox)(cosx/sinx)- cos^2x/sinx= 1/sinx- cos^2x/sinx
    = (1- cos^2x)/sinx

    Yes, that's correct.

    Again, you are not being careful with parentheses. I think you mean
    (1+ sinx)/cosx+ cosx/(1+ sin(x)) bit what you wrote is 1+ (sinx/cosx)+ cosx+ sin(x).

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