SOLUTION: prove: sin(n+1)x sin(n+2)x+cos(n+1)x cos(n+2)x=cosx

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Question 815261: prove: sin(n+1)x sin(n+2)x+cos(n+1)x cos(n+2)x=cosx
Answer by lwsshak3(11628) About Me  (Show Source):
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prove: sin(n+1)x sin(n+2)x+cos(n+1)x cos(n+2)x=cosx
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Identity: cos(s-t)=cos(s)x*cos(t)x+sin(s)x*sin(t)x
cos(s-t)=cos(s)x*cos(t)x+sin(s)x*sin(t)x
cos((n+1)x)-((n+2)x=cos(n+1)x*cos(n+2)x+sin(n+1)x*sin(n+2)x
cos((nx+x)-(nx+2x))=cos(n+1)x*cos(n+2)x+sin(n+1)x*sin(n+2)x
cos((nx+x)-(nx+2x))=cos(nx+x-nx-2x)=cos(-x)=cos(x)
verified: left side=right side