Posted by **John** on Monday, February 10, 2014 at 8:08pm.

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 -
**Steve**, Monday, February 10, 2014 at 8:34pm
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 -
**John**, Monday, February 10, 2014 at 9:03pm
Wow, I tried that but I messed up signs! Thanks!

- Precalculus -
**John**, Monday, February 10, 2014 at 9:09pm
Oops I meant sum and difference

- Precalculus -
**Steve**, Tuesday, February 11, 2014 at 12:27am
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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