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Verify the identity help needed?

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(sin theta-cos theta)^2= 1-sin 2 theta

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  1. ( sin theta- cos theta)^2= 1- sin 2 theta

    sin ^2( theta)-2sin theta cos theta+ cos^2 theta= 1- sin 2 theta

    arranging:

    sin ^2( theta)+ cos^2 theta-2sin theta cos theta= 1- sin 2 theta

    since sin^2 theta+ cos^2 theta = 1

    then

    1- 2 sin theta cos theta= 1- sin 2 theta

    since  2 sin theta cos theta=1-  sin 2 theta

    therefore it becomes

    1-sin 2 theta= 1- sin 2 theta

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