Proof this, please?

1 - (sin^2x tanx/(tanx+1)) - (cos^2x/(tanx+1)) = sinx cosx

Show your work. Please don't skip any steps.

2 Answers

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  • 2 years ago
    Favorite Answer

    LHS = 1 - [ (sin²x tanx ) / (tanx + 1) ] -

    [ cos²x / (tanx + 1) ]

    = [( tanx + 1) - sin²x tanx - cos²x ] / (tanx + 1)

    = [ (tanx - sin²x tanx) + ( 1 - cos²x ) ] / (tanx+1)

    = [ tanx ( 1 -sin²x) + sin²x ] / (tanx + 1)

    = ( tanx cos²x + sin²x ) / (tanx +1)

    =[ (sinx / cosx ) cos²x + sin²x ] /

    [ (sinx /cosx) + 1 ]

    = [ sinx cosx + sin²x ] / [ (sinx + cosx)/cosx]

    = sinx ( cosx + sinx) / [ (sinx + cosx)/cosx]

    = sinx cosx = RHS........ proved

    I hope this helps !

    Source(s): Note: ● 1- sin²x = cos²x ● 1- cos²x = sin²x ● tanx = sinx / cosx
  • ?
    Lv 6
    2 years ago

    I proofed what you posted.

    All appears in order, except the grammar.

    I think you want someone to prove the proof provided.

    • I DON'T CARE. IT'S MATH HOMEWORK NOT ENGLISH HOMEWORK IF YOU CAN'T TELL.

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