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Question

If tan x=ab, show that a sin x-b cos xa sin x+b cos x=a2-b2a2+b2.

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Solution

LHS:asinx-bcosxasinx+bcosxDividing by bcosx:= atanxb-1atanxb+1Substituting the value of tanx= a2-b2a2+b2= RHS
Hence proved.

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