Question

证明COS（X+Y）COS（X-Y）=COS^2X-SIN^2Y

Answer 1

COS（X+Y）COS（X-Y）

=(COSX*COSY-SINX*SINY)(COSX*COSY+SINX*SINY)

=(COSX*COSY)^2-(SINX*SINY)^2

=COS^2 X(1-SIN^2 Y)-(1-COS^2 X)SIN^2 Y

=COS^2 X -COS^2 X*SIN^2 Y-SIN^2 Y +COS^2 X SIN^2 Y

=COS^2X-SIN^2Y