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Math Help - Trig Expressions and Identities.

  1. #1
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    Trig Expressions and Identities.

    Hey all if you could please help i would be so grateful!

    1. Mulitply and simplify-
    cosXsinX(secX-cscX)
    I got 1 by turning it into 1 but Im not 100% sure.

    2. Simplify expression-
    (15tanXcscX-3cscX)/(9tanXcscX-3cscX)

    3. Establish the Indentity
    (1-sin2X)/(sinX-cscX)=-sinX

    4. Establish the identity
    cotX(cotX+tanX)=csc^2X

    5. Establish the indentity
    1- (cos^2X/1+sinX)=sinX

    6. (sinX)/(1+cosX)+(1+cosX)/(sinX)= 2cscX


    I've been working on this forever and cant seem to get these answers, any help is awesome! THANKS SO MUCH
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  2. #2
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    For the first one, I'm not sure how you got 1 hehe

    cos(x)sin(x) (sec(x)-csc(x))

    (cos(x)sin(x)/cos(x)) - (cos(x)sin(x)/sin(x))

    sin(x) - cos(x)


    and for the fourth one..

    Cot(x) (cot(x)+tan(x)) = csc^2(x)

    multiply out..

    cot^2(x) + (cot(x)tan(x)) = csc^2(x)

    cot^2(x) + 1 = csc^2(x)

    which is a common trig identity


    and for the last one...

    make a common denominator, and remember that sin^2(x) + cos^2(x) = 1. then just do some algebra magic
    Last edited by coolguy99; March 22nd 2009 at 08:12 PM.
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  3. #3
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    Quote Originally Posted by amanda0603 View Post
    Hey all if you could please help i would be so grateful!

    1. Mulitply and simplify-
    cosXsinX(secX-cscX)
    I got 1 by turning it into 1 but Im not 100% sure.
    sec(x)-csc(x) = \frac{1}{cos(x)} - \frac{1}{sin(x)}. Get the same denominator which will then cancel with the cos(x)sin(x) also present

    \frac{1}{cos(x)} - \frac{1}{sin(x)} = \frac{sin(x)-cos(x)}{cos(x)sin(x)} so the final answer is

    \frac{cos(x)sin(x)(sin(x)-cos(x)}{cos(x)sin(x)} = sin(x)-cos(x)

    2. Simplify expression-
    (15tanXcscX-3cscX)/(9tanXcscX-3cscX)
    Factor and cancel:
    \frac{3csc(x)(5tan(x)-1)}{3csc(x)(3tan(x)-1)} = \frac{5tan(x)-1}{3csc(x)-1}

    3. Establish the Indentity
    (1-sin2X)/(sinX-cscX)=-sinX
    4. Establish the identity
    cotX(cotX+tanX)=csc^2X
    cot(x)+tan(x) = \frac{1+tan^2(x)}{tan(x)} = \frac{sec^2(x)}{tan(x)}

    \frac{cot(x)sec^2(x)}{tan(x)} = \frac{cos^2(x)sec^2(x)}{sin^2(x)} = csc^2(x)

    5. Establish the indentity
    1- (cos^2X/1+sinX)=sinX
    \frac{cos^2(x)}{1+sin(x)} = \frac{1-sin^2(x)}{1+sin(x)}

    use the difference of two squares on the numerator and 1+sin(x) should cancel
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