Question

Упростите выражения:

1)cos(a-β)-cos a cos β=

2)sin a cos β-sin (a-β)=

3)sin(a+β)-sin(a-β)=

 

Answer 1

1)cos(a-β)-cos a cos β=cos a cos β+sin a sin β-cos a cos β=sin a sin β

2)sin a cos β-sin (a-β)=sin a cos β -( sin a cos β-cos a sin β)=

   =sin a cos β -sin a cos β+cos a sin β=cos a sin β

3)sin(a+β)-sin(a-β)=sin a cos β +cos a sin β-( sin a cos β-cos a sin β)=

  = sin a cos β +cos a sin β- sin a cos β+cos a sin β=2cos a sin β