Question

How do you verify `cos (x-y) - cos (x+y) = 2 sin x sin y`?

Answer 1

see below

Explanation:

Use Properties: `cos(A+B)=cosAcosB-sinAsinB`
`cos(A-B)=cosAcosB+sinAsinB`

Left Side: `=cos(x-y)-cos(x+y)`

`=cosxcosy+sinxsiny-(cosxcosy-sinxsiny)`

`=cosxcosy+sinxsiny-cosxcosy+sinxsiny`

`=2sinxsiny`

`=`Right Side