Question

Упростить выражение: срочно!$( frac{cos2 alpha }{sin alpha -cos alpha } )^{2} - sin2 alpha$

Answer 1

$( frac{cos2 alpha }{sin alpha -cos alpha } )^{2} -sin2 alpha = ( frac{ cos^{2} alpha - sin^{2} alpha }{sin alpha -cos alpha } ) ^{2} -sin2 alpha =$
$( frac{(cos alpha -sin alpha )*(cos alpha +sin alpha )}{-(cos alpha -sin alpha )} )^{2} -sin2 alpha = (-(cos alpha +sin alpha) )^{2} -sin2 alpha =$
$= cos^{2} alpha +2sin alpha *cos alpha + sin^{2} alpha -2sin alpha *cos alpha = cos^{2} alpha + sin^{2} alpha =1$