Expert: Steve Holleran - 12/7/2007

Question
     1           Cos a cos b
____________ =  _____________
tan a + tan b    sin( a+b)      Verify the Indentity

Answer
Hi Robert,

This one is not as difficult as it looks.

On the left, let's break the tangents into sines and cosines:

  1 / (tan a + tan b) = 1 / ( sin a/cos a  + sin b/ cos b)

Now multiply the top and bottom of this by cos a * cos b:

= (cos a * cos b) / (sin a cos b + sin b cos a)

the bottom is now the identity for sin(a+b), so you have

 (cos a cos b) / sin(a + b)

which is the result you wanted.

Hope this helps.
Steve