Question
Fri June 01, 2012 By: Aarthi Vishwanathan
 

if tanx+tany=a and cotx+coty=b prove that cot(x+y)=(1/a)-(1/b)

Expert Reply
Sun June 03, 2012
R.H.S.= 1/a - 1/b
= 1/ tanx+tany - 1/ coty+cotx
= cosx cosy/ sinx cosy + cosx siny - sinx siny/ sinx cosy + cosx siny
= cosxcosy-sinxsiny/ sinxcosy+cosxsiny 
= cos (x+y)/ sin(x+y)
= cot (x+y) 
= L.H.S.
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