Hello.

I was proving that sin α - β = sin α * cos β - cos α * sin β but getting something wrong.

OP_α = (cos α, sin α)
OP_β = (cos β, sin β)
|OP_α × OP_β| = |OP_α| * |OP_β| * sin (γ)
|OP_α| = |OP_β| = 1
γ = α - β
Hence, |OP_α × OP_β| = sin (α - β)
Since, |A × B| = A_x * B_y - A_y * B_x
|OP_α × OP_β| = cos α * sin β - sin α * cos β
Hence, sin (α - β) = cos α * sin β - sin α * cos β

But all formulas in internet say that sin α - β = sin α * cos β - cos α * sin β , i.e reverse of what I wrote above. Can someone find my mistake?