Posted by John on .
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,
using the halfangle formulas,
sin(x)sin(y) = 2 cos((x+y)/2)sin((xy)/2)
cos(x)cos(y) = 2sin((x+y)/2)sin((xy)/2)
tada! 
Precalculus 
John,
Wow, I tried that but I messed up signs! Thanks!

Precalculus 
John,
Oops I meant sum and difference

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