Simplify sin^2(π/8 + x/2) - sin^2(π/8 - x/2)?

thanks! :)

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  • Anonymous
    1 decade ago
    Favorite Answer

    Using the addition/subtraction formulas for sine you get:

    sin(π/8 + x/2) = sin(π/8)cos(x/2) + cos(π/8)sin(x/2)

    sin(π/8 - x/2) = sin(π/8)cos(x/2) - cos(π/8)sin(x/2)

    The original expression factors into:

    [sin(π/8 + x/2) + sin(π/8 - x/2)] [sin(π/8 + x/2) - sin(π/8 - x/2)]

    So this is:

    [ 2sin(π/8)cos(x/2) ] [ 2cos(π/8)sin(x/2) ]

    2sin(π/8)cos(π/8) * 2sin(x/2)cos(x/2)

    Since sin(2x) = 2sin(x)cos(x), this becomes

    sin(π/4)sin(x)=

    (√2/2)sin(x)

  • norman
    Lv 7
    1 decade ago

    factor the expression like a^2 - b^2=(a+b)(a-b)

    (sin(pi/8 + x/2)+sin(pi/8- x/2))(sin(pi/8+x/2)-sin(pi/8-x/2)

    use the multiple angle formula to cont...

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