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

Asked by Aarthi Vishwanathan | 1st Jun, 2012, 08:43: PM

Expert Answer:

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.

Answered by  | 3rd Jun, 2012, 04:08: PM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.