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Math Help - Verifying Identites

  1. #1
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    Verifying Identites

    Verify the following identity:

    2sin^2x +cos2x
    _______________. =cosx
    secx


    or

    2 sine squared x plus cosine 2 x divided by secant x

    Can anyone do this problem for me and go over the steps...I've been going at it for a while and can't solve this ish.......I've used so many reciprocal identities and pythagreon identites and I still can't figure it out.



    Thanks!
    Last edited by sabes; February 12th 2009 at 06:47 PM.
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  2. #2
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    Quote Originally Posted by sabes View Post
    Verify the following identity:

    2sin^2x +cos2x
    _______________
    secx


    or

    2 sine squared x plus cosine 2 x divided by secant x

    Can anyone do this problem for me and go over the steps...I've been going at it for a while and can't solve this ish.......I've used so many reciprocal identities and pythagreon identites and I still can't figure it out.



    Thanks!
    what you posted is not an identity, it is a trigonometric expression.

    an identity is an equation. so, something is missing or you misread the instructions on what to do with the expression.
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  3. #3
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    oh crap. I left out the "=cosx" bit at the end!

    I'm sorry...could you still help?

    Thanks

    I'm sorry if I wasted any of your time if you were confused. I feel like a dummy. Sorry
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  4. #4
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    try this ...

    change \cos(2x) in the numerator to \cos^2{x} - \sin^2{x} and combine like terms.

    ... see what happens.
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  5. #5
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    [size=3]Hello, sabes!

    Verify the following identity: . \frac{2\sin^2\!x +\cos2x}{\sec x} \:=\:\cos x

    We're expected to know this identity: . \cos2x \:=\:2\cos^2\!x-1


    So: . \frac{2\sin^2\!x + \cos2x}{\sec x} \;=\;\frac{2\sin^2\!x + (2\cos^2\!x - 1)}{\sec x} \;=\;\frac{2\overbrace{(\sin^2\!x+\cos^2\!x)}^{\te  xt{This is 1}} - 1}{\sec x}

    . . = \;\;\frac{2-1}{\sec x} \;\;=\;\;\frac{1}{\sec x} \;\;=\;\;\cos x

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  6. #6
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    Oh snap!

    Thanks a ton guys.

    I need help with one more if ya don't mind:

    (sinx+cosx)^2 =1+sin2x

    Now I foiled the first half of the equation and got stuck here:

    Sin^2x + 2sinxcosx + cos^2x =1+sin2x
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  7. #7
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    Quote Originally Posted by sabes View Post
    Oh snap!

    Thanks a ton guys.

    I need help with one more if ya don't mind:

    (sinx+cosx)^2 =1+sin2x

    Now I foiled the first half of the equation and got stuck here:

    Sin^2x + 2sinxcosx + cos^2x =1+sin2x
    look at the left side.

    you are expected to know these two identities ...

    \sin^2{x} + \cos^2{x} = 1

    2\sin{x}\cos{x} = \sin(2x)
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