Prove the trig identity: cos(-x)+cos(pi-x)=cos(pi+x) + cos(x)

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`cos(-x) = cos(x)`

`cos(pi-x)=-cos(x)`

`cos(pi+x)=-cos(x)`

Therefore:

`cos(x)-cos(x)=-cos(x)+cos(x)`

`0=0`

Since the left side equals the right side, the original equation is true.

Sources:

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