Question

Verify that: cos(x+y)cos(x-y)=cos^2x-sin^2y

Using trig idenities, I can get to: cos^2xcos^2y-sin^2xsin^2y but I can't figure out how to get rid of sin^2x and cos^2y. Anybody?

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