how to prove it?
plz help me!!
3 Answers

cot(x+y) = (cotxcoty1)/(cotx+coty)?
Girl, please read patiently. It is NOT tough but needs patience.
LHS = cot(x+y)
= cos(x+y) / sin(x+y)
= [(cosxcosy  sinxsiny) / (sinxcosy + cosxsiny)]
Divide numerator and denominator by sinx*siny, we get
(cotxcoty1)/(coty+cotx),
= (cotxcoty1)/(cotx+coty) = RHS

Y Cot X

cot (x+y) = 1 / tan (x+y) = 1/ [(tan x + tan y)/(1  tan x tan y)] = (1  tan x tan y) / (tan x + tan y) = (1  (1/(cot x cot y))) / (1/cot x + 1/cot y) = ((cot x cot y  1)/(cot x cot y)) / ((cot x + cot y)/(cot x cot y)) = (cot x cot y  1) / (cot x + cot y) Proved !!!