Prove that : `cos((3pi)/4 - x) - sin((3pi)/4 + x) = -sqrt 2*(cosx - sinx)`

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The identity `cos((3pi)/4 - x) - sin((3pi)/4 + x) = -sqrt2*(cos x - sin x)` has to be proved.

`cos((3pi)/4 - x) - sin((3pi)/4 + x)`

= `cos((3pi)/4)*cos x + sin((3pi)/4)*sin x - sin((3pi)/4)*cos x - cos((3pi)/4)*sin x`

= `(-1/sqrt2)*cos x + (1/sqrt 2)*sin x - (1/sqrt 2)*cos x - (-1/sqrt 2)*sin x`

= `(-1/sqrt2)*cos x + (1/sqrt 2)*sin x - (1/sqrt 2)*cos x + (1/sqrt 2)*sin x`

= `(-2*cos x)/sqrt2 + (2*sin x)/sqrt 2`

= `-sqrt 2*cos x + sqrt 2*sin x`

= `-sqrt 2*(cos x - sin x)`

This proves that `cos ((3*pi)/4 - x) - sin((3*pi)/4+x) = -sqrt 2*(cos x - sin x) `

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