TanX+TanY/CotX+CotY = Tanx Tany
2007-06-03 16:22:26 · 3 answers · asked by yes!!!!! 1 in Science & Mathematics ➔ Mathematics
LHS = (TanX+TanY)/(CotX+CotY )
Numerator = sinx / cosx + siny / cosy
= (sinxcosy + sinycosx) / (cosxcosy)
Denominator = cosx/ siny+ cosy/ siny
= (sinxcosy + sinycosx) / (sinxsiny)
Num / Den = (sinx siny) / (cosx cosy)
= tanx tany
2007-06-03 16:29:34 · answer #1 · answered by Dr D 7 · 1⤊ 0⤋
LHS
= (TanX+TanY)/(CotX+CotY)
= (TanX+TanY)/[(1/TanX)+(1/TanY)]
= (TanX+TanY)/[(TanY+TanX)/TanXTanY]
= TanXTanY(TanX+TanY) / (TanX+TanY)
= TanX TanY
= RHS
(QED)
2007-06-03 23:27:44 · answer #2 · answered by Kemmy 6 · 0⤊ 0⤋
Consider LHS:-
Numerator = N
N = sin x / cosx + sin y / cosy
N = (sin x.cosy + cos x.sin y) / (cos x.cos y)
Denominator = D
D = cos x /sin x + cos y / sin y
D = (sin y.cos x + cos y.sin x) / sin x.sin y
N / D = (1 / (cos x.cos y)). (sin x. sin y)
N / D = tan x.tan y
2007-06-04 08:35:00 · answer #3 · answered by Como 7 · 0⤊ 0⤋