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

Algebra ->  Geometry-proofs -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
1-[cos(x)-sin(x)]ē = sin(2x)

To square a binomial write it twice and use FOIL:

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

1-[cosē-cos(x)sin(x)-sin(x)cos(x) + sinē(x)]

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

1-[cosē(x)-2sin(x)cos(x) + sinē(x)]

     Since cosē(x)+sinē(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