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f(x)=(1)/(sin(x))|[y+z,x,y],[z+x,z,x],[x...

f(x)=(1)/(sin(x))|[y+z,x,y],[z+x,z,x],[x+y,y,z]|=(x+y+z)(x-z)^(2)

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y+z,x,yz+y,z,xx+y,y,z]|=(x+y+z)(x-z)^(2)

show that |[y+z ,x, y],[ z+x, z, x],[x+y, y ,z]|=(x+y+z)(x-z)^2

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x+y+z,-z,-y-z,x+y+z,-x-y,-x,x+y+z]|=2(x+y)(y+z)(z+x)

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Prove the identities: |[z, x, y],[ z^2,x^2,y^2],[z^4,x^4,y^4]|=|[x, y, z],[ x^2,y^2,z^2],[x^4,y^4,z^4]|=|[x^2,y^2,z^2],[x^4,y^4,z^4],[x, y, z]| =x y z (x-y)(y-z)(z-x)(x+y+z)

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