SOLUTION: Please prove the following identity 1-(cosx-sinx)^2=sin2x I attempted it but I only get as far as opening the brackets. And I'm not even sure if I'm doing that correct. Please

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Question 827723: Please prove the following identity
1-(cosx-sinx)^2=sin2x
I attempted it but I only get as far as opening the brackets. And I'm not even sure if I'm doing that correct. Please help..
Answer by Edwin McCravy(20081)   (Show Source): You can put this solution on YOUR website!
1-[cos(x)-sin(x)]² = sin(2x)

To square a binomial write it twice and use FOIL:

1-[cos(x)-sin(x)][cos(x)-sin(x)]

1-[cos²-cos(x)sin(x)-sin(x)cos(x) + sin²(x)]

     The two terms in the middle are the same 
     so they add together:

1-[cos²(x)-2sin(x)cos(x) + sin²(x)]

     Since cos²(x)+sin²(x)=1

1-[1-2sin(x)cos(x)]

1-1+2sin(x)cos(x)

2sin(x)cos(x)

    Since sin(2x) = 2sin(x)cos(x)

sin(2x)

Edwin
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