Question

已知2cosx+cosy=2/3,2sinx-siny=3/4,求cos(x+y).

Answer 1

(2cosx+cosy)^2+(2sinx-siny)^2

=4(cosx)^2+4(sinx^2+(cosy)^2+(siny)^2+4(cosxcosy-sinxsiny)

=5+4cos(x+y)

=4/9+9/16

=145/144

cos(x+y)=-575/576