Question

если
$cos( alpha ) - sin( alpha ) = 0.2$
то найдите
cos³A－sin³A=

Answer 1

$cosalpha -sinalpha=0,2\\ (cosalpha -sinalpha)^2=0,2^2\\ cos^2alpha-2cosalphasinalpha+sin^2alpha=0,04\\ (cos^2alpha+sin^2alpha)-2cosalphasinalpha=0,04\\ 1 -2cosalphasinalpha =0,04\ \ -2cosalpha sinalpha =0,04-1\ \ -2cosalphasinalpha =-0,96 \ \ cosalpha sinalpha =0,48$

$cos^3alpha -sin^3alpha =(cosalpha -sinalpha )(cos^2alpha +cosalpha sinalpha +sin^2alpha )=\ \ =(cosalpha -sinalpha )(cos^2alpha -2cosalpha sinalpha +sin^2alpha+3cosalpha sinalpha )=\ \ =(cosalpha -sinalpha )((cosalpha -sinalpha )^2+3cosalpha sinalpha) =\ \ =0,2cdot(0,2^2+3cdot0,48)=0,2cdot(0,04+1,44)=0,2cdot1,48=0,296$