Question

 ............Доказать тождество........

Answer 1

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Answer 2

$cfrac{(sin alpha -cos alpha )^2-1}{tg alpha -sin alpha cos alpha } = cfrac{sin ^2alpha+cos^2 alpha -2sin alpha cos alpha -1}{ frac{sin alpha }{cos alpha } -sin alpha cos alpha } = \ = cfrac{1 -2sin alpha cos alpha -1}{ frac{sin alpha-sin alpha cos^2 alpha }{cos alpha } } = cfrac{ -2sin alpha cos alpha cdot cos alpha }{ sin alpha(1-cos^2 alpha ) } = cfrac{ -2 cos^2alpha }{1-cos^2 alpha}= \ =cfrac{-2 cos^2alpha }{ sin^2 alpha } =-2ctg^2 alpha$