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Math Help - trigonometric identity problem

  1. #1
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    trigonometric identity problem

    Hello,

    i am having some trouble figuring out this problem, any help would be great!

    (cosx+sinx+1)(cosx+sinx-1)=sin2x
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  2. #2
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    Hi there Aerowen, here's my take.

    You need to expand out the brackets, the problem should fall out for you!

    (\cos x+\sin x+1)(\cos x+\sin x-1)

    =\cos^2 x+\cos x \sin x-\cos x+\cos x \sin x+ \sin^2-\sin x +  \cos x+\sin x-1

    Now grouping some like terms.

    =\cos^2 x+ \sin^2+\cos x \sin x+\cos x \sin x-\sin x +\sin x+  \cos x-\cos x-1

    Cancelling

    =\cos^2 x+ \sin^2+2\cos x \sin x-1

    Applying the pythagorean identity

    =1+2\cos x \sin x-1

    =2\cos x \sin x

    =2 \sin x\cos x

    = \sin 2x
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