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

Question

27096 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-05-13T15:24:37

see below

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

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