Respuesta :

calculista

Answer:

see the procedure

Step-by-step explanation:

we know that

[tex]cos(X - Y) = cosX cosY + sinX sinY\\cos(X + Y) = cosX cosY - sinX sinY[/tex]

so

[tex]cos(X - Y)-cos(X + Y)=cosX cosY + sinX sinY-(cosX cosY - sinX sinY)[/tex]

[tex]cos(X - Y)-cos(X + Y)=cosX cosY + sinX sinY-cosX cosY + sinX sinY[/tex]

[tex]cos(X - Y)-cos(X + Y)=sinX sinY+ sinX sinY[/tex]

[tex]cos(X - Y)-cos(X + Y)=2sinX sinY[/tex] ----> is verified