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Math Help - Advanced problem!!

  1. #1
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    Oct 2009
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    Unhappy Advanced problem!!

    Please help me prove this identity:

    2Sin^2(x+pi/4) = 1 + Sin2x

    I was thinking that I have to include cofunctions somehow, but have no idea how! This has been bugging me for too long!

    Thanks!
    Andrew
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  2. #2
    Member
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    May 2009
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    New Delhi
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    Quote Originally Posted by Android View Post
    Please help me prove this identity:

    2Sin^2(x+pi/4) = 1 + Sin2x

    I was thinking that I have to include cofunctions somehow, but have no idea how! This has been bugging me for too long!

    Thanks!
    Andrew
    use identity
     \cos {2x}= 1-2 \sin^2 {x}
    if stuck look spoiler
    Spoiler:

     \cos {2x}= 1-2 \sin^2 {x} \quad \Rightarrow \quad \boxed {2 \sin^2 {x} = 1-\cos {2x}}
     \therefore LHS=2Sin^2(x+pi/4)=1-\cos { \left ( 2 \cdot (x+ \frac {pi}{4}) \right ) }
    =1- \cos { \left ( 2x+\frac{\pi}{2} \right )}=1+\sin {2x} =RHS
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  3. #3
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    That all makes perfect sense! Thank you SO much!
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