Обоснуйте тождество: [tex]sin^2( alpha -2 beta ) - cos^2 alpha -

Используем формулы:
cosa*cosb=1/2*(cos(a-b)+cos(a+b))
cos2a=2cosa-1
sina+cosa=1
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-2cosa*cos2b*cos(a-2b)=-2*1/2(cos(a-2b)+cos(a+2b))*cos(a-2b)=
=-cos(a-2b)-cos(a+2b)*cos(a-2b)=
=sin(a-2b)-1-1/2*(cos(a+2b-a+2b)+cos(a-2b+a-2b))=
=sin(a-2b)-1-1/2cos4b-1/2cos2a=
=sin(a-2b)-1-1/2*(2cos2b-1)-1/2*(2cosa-1)=
=sin(a-2b)-1-cos2b+1/2-cosa+1/2=sin(a-2b)-cos2b-cosa

sin(a-2b)-cosa-cos2b=sin(a-2b)-cos2b-cosa