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Precalculus

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Show that
cot((x+y)/2)=-(sin(x)-sin(y))/(cos(x)-cos(y))
for all values of x and y for which both sides are defined.

  • Precalculus -

    using the half-angle formulas,

    sin(x)-sin(y) = 2 cos((x+y)/2)sin((x-y)/2)
    cos(x)-cos(y) = -2sin((x+y)/2)sin((x-y)/2)

    ta-da!

  • Precalculus -

    Wow, I tried that but I messed up signs! Thanks!

  • Precalculus -

    Oops I meant sum and difference

  • Precalculus -

    No, I meant sum and difference. I started out trying the half-angle for tangent, but got bogged down. Then I saw the sums on the right and went the easy way.

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