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If tan B = mSinACosA/ 1-mSin^2A , prove that tan(A-B)=(1-m)tanA
ANALYSE THE QUESTION: tan B = mSinACosA/ 1-mSin^2A we have to find tan(A-B) which is equal to(tanA – tanB )/(1+tanAtanB) ------------(1)IN THIS QUESTION, JUST PUT THE VALUE OF tanB in upper equation (1)after solving, you will get [tanA(1-msin2A) – msinAcosA ] / [1- msin2A + tanAmsinAcosA ]JUST LOOK AT THE DENOMINATOR, IT IS BECOMING 1 (write tanA = sinA/cosA AND msin2A term will be cancelled )NOW YOU ARE LEFT WITH NUMERATOR, mutiply and divide msinAcosA by cosA AND take tanA common.tanA [1-m(sin2A + cos2A )tanA [ 1-m(1) ]
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