Cosx+siny=1/2 cosy-sinx=√2/2 sin(x-y)=?
(Cosx+siny)^2=(1/2)^2 ( her iki tarafinin karesini aldik)
(cosx)^2 + 2.cosx.siny+(siny)^2=1/4 (*)
ayni mantik ile
(cosy-sinx)^2=(√2/2)^2
(cosy)^2 - 2.cosy.sinx+(sinx)^2=2/4=1/2 (**)
(*)+(**)
(cosx)^2 + 2.cosx.siny+(siny)^2+(cosy)^2 - 2.cosy.sinx+(sinx)^2=1/4 +1/2
(cosx)^2+(sinx)^2=1 ve (siny)^2+(cosy)^2=1
2+2.cosx.siny- 2.cosy.sinx=3/4
2- 3/4= 2.cosy.sinx-2.cosx.siny
5/4=2.(sinx.cosy-siny.cosx)
5/8=(sinx.cosy-siny.cosx)
sin(x-y)=sinx.cosy-siny.cosx ( oldugundan)
sin(x-y)=5/8