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Math Help - Proving Trig identities help!

  1. #1
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    Proving Trig identities help!

    Hi

    having trouble with the below trig identity just cant seem to get round it

    prove the trigonometric identity

    sin^2A(secA+cosecA)/1+tanA = sinA

    i admit not the best at trig, just not sure what to do with the bottom half any help would be appreciated

    webb
    Last edited by mr fantastic; March 28th 2011 at 01:20 PM. Reason: Deleted excess ! in title.
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  2. #2
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    I assume this is your equation...

    \displaystyle \frac{\sin^2{A}(\sec{A} + \csc{A})}{1 + \tan{A}} \equiv \sin{A}

    Brackets MUST be used where they are needed...


    Anyway...

    \displaystyle \frac{\sin^2{A}(\sec{A} + \csc{A})}{1 + \tan{A}} \equiv \frac{\sin^2{A}\left(\frac{1}{\cos{A}} + \frac{1}{\sin{A}}\right)}{1 + \frac{\sin{A}}{\cos{A}}}

    \displaystyle \equiv \frac{\sin^2{A}\left(\frac{\sin{A} + \cos{A}}{\sin{A}\cos{A}}\right)}{\frac{\cos{A} + \sin{A}}{\cos{A}}}

    \displaystyle \equiv \frac{\frac{\sin{A}(\sin{A} + \cos{A})}{\cos{A}}}{\frac{\cos{A} + \sin{A}}{\cos{A}}}

    \displaystyle \equiv \frac{\sin{A}(\sin{A} + \cos{A})}{\cos{A} + \sin{A}}

    \displaystyle \equiv \sin{A}.
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  3. #3
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    Thankyou

    Thankyou, that is exactly what I was after, the step by step helped brilliantly

    much appreciated
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