catphalenovgmm8 catphalenovgmm8
  • 25-02-2018
  • Mathematics
contestada

prove the identity cos(x-y)-cos(x+y)=2sinxsiny

Respuesta :

calculista
calculista calculista
  • 21-10-2019

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

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