Question

If tanA + sinA =m & tanA- sinA =n then find m^2-n^2=4m

Answer 1

If tanA + sinA = m and tanA – sinA = n, show that m2 – n2 = 4√(mn)Solution :-

LHS = m2 – n2 = (tanA + sinA)2 – (tanA – sinA)2

= tan2A + sin2A + 2tanAsinA – tan2A – sin2A + 2tanAsinA

= 4tanA.sinA

RHS = 4√(mn) = 4√(tanA + sinA).(tanA – sinA )

= 4√(tan2A – sin2A = 4√(sin2A/cos2A – sin2A)

= 4√{(sin2A – sin2Acos2A)/cos2A}

= 4√{sin2A(1 – cos2A)/cos2A}

= 4√(sin2A.sin2A/cos2A)

= 4(sinA.sinA/cosA)

= 4.tanA.sinA = LHS