sin(α-β)怎么用cos(α-β)\cos(α+β)推导

Question

sin(α-β)怎么用cos(α-β)\cos(α+β)推导

Answer 1

已知：
cos (α +β) = cos α cos β -sin α sin β,
sin (π/2 -α) =cos α,
cos (π/2 -α) =sin α.
则
sin (α -β) =cos [ π/2 -(α -β) ]
=cos [ (π/2 -α)+β ]
=cos (π/2 -α) cos β -sin (π/2 -α) sin β
=sin α cos β -cos α sin β.
= = = = = = = = =
sin (α +β) 可用 cos (α -β) 和诱导公式推导.