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Math Help - Double and half angle identities?

  1. #1
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    Double and half angle identities?

    Can anyone help me verify these two identities

    1. csc2x= 1/2 secx cscx I am not sure how to start this one

    My second one I am not sure if I have done it right?

    (sinx+cosx)^2-1= sin2x
    (sinx+cosx) (sinx+cosx)-1
    sinx^2+sinxcosx+sinxcosx+cosx^2-1
    1+2sincosx-1=sin2x
    2sinxcosx=sin2x
    sin2x=sin2x Did I do this right?
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  2. #2
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    Quote Originally Posted by homeylova223 View Post
    (sinx+cosx)^2-1= sin2x
    (sinx+cosx) (sinx+cosx)-1
    sinx^2+sinxcosx+sinxcosx+cosx^2-1
    1+2sincosx-1=sin2x
    2sinxcosx=sin2x
    sin2x=sin2x Did I do this right?
    Right!

    A hint for the first one -- it says:

    \displaystyle \frac{1}{\sin{2x}} = \frac{1}{2\sin{x}\cos{x}}
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  3. #3
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    Quote Originally Posted by homeylova223 View Post
    Can anyone help me verify these two identities

    1. csc2x= 1/2 secx cscx I am not sure how to start this one

    \displaystyle \csc 2x = \frac{1}{\sin 2x} = \frac{1}{2\sin x \cos x} = \frac{1}{2}\csc x \sec x
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