Question

(sin^4 a - cos^4 a + cos^2a) / (2*(1-cosa))

Answer 1

$frac{sin^4 alpha -cos^4 alpha +cos2 alpha }{2(1-cos alpha )}=frac{sin^4 alpha -cos^4 alpha +cos^2 alpha-sin^2 alpha }{2(1-cos alpha )}=\\=frac{sin^2 alpha (sin^2 alpha -1)+cos^2 alpha (1-cos^2 alpha )}{2(1-cos alpha )}=frac{sin^2 alpha (sin^2 alpha -1)+cos^2 alpha sin^2 alpha }{2(1-cos alpha )}=\\=frac{sin^2 alpha (sin^2 alpha -1+cos^2 alpha)}{2(1-cos alpha )}=frac{sin^2 alpha (1 -1)}{2(1-cos alpha )}=0.$

Answer 2

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