How do you prove $cos (pi-x) =- cosx$ ?

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Answer 1 · 2016-01-31T22:20:51

Use the cosine subtraction formula to expand the term.

Use the cosine subtraction formula:

$cos(alpha-beta)=cos(alpha)cos(beta)+sin(alpha)sin(beta)$

When applied to $cos(pi-x)$ , this gives

$cos(pi-x)=cos(pi)cos(x)+sin(pi)sin(x)$

Simplify.

$cos(pi-x)=(-1)cos(x)+(0)sin(x)$

$cos(pi-x)=-cos(x)$

How do you prove cos (pi-x) =- cosxcos (pi-x) =- cosx?