Question

Доказать тождество(срочно помогите)
(sinx+siny)^2+(cosx+cosy)^2=4cos^2 x-y/2

Answer 1

(sinx+siny)^2+(cosx+cosy)^2=2+2(sinxsiny+cosxcosy)=2+2cos(x-y)=2(1+cos(x-y))=

=4(1+cos(x-y)/2)=4cos^2(x-y)/2)