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.