(tanx + tany)/(cotx + coty) =
(tanx)(tany)
We will start from the left
side.
We know that:
tanx =
sinx/cosx
cot(x) =
cosx/sin(x)
==> (tanx+tany)/(cot(x)+cot(y)) =
(sin(x)/cosx + siny/cosy)/(cosx/sinx + cosy/siny).
=[ (
sinx*cosy + siny*cosx)/cosx*cosy]/ (cosx*siny+sinx*cosy)/
sinx*siny)
Now we will reduce like
terms.
==> (1/cosx*cosy) /
(1/sinx*siny)
==> sinx*siny/
cosx*cosy
==> sinx/cosx * siny / cosy = tanx * tany
..............q.e.d
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