How can I prove the identity for cos(x+pi)=-cos x ?

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How can I prove the identity for cos(x+pi)=-cos x ?

Using the angle sum and angle difference formulas

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Answer 1 · 2018-06-04T22:33:01

Using the angle addition formula for cosine.

Explanation:

The angle addition formula for cosine is
$cos (α + β) = cos α cos β - sin α sin β$ $cos(alpha+beta)=cosalphacosbeta-sinalphasinbeta$ , and we can use this to prove that $cos (π + x) = - cos (x)$ $cos(pi+x)=-cos(x)$ .

$cos (π + x) = cos π cos x - sin π sin x = (cos x \cdot - 1) - (sin x \cdot 0) = - cos x$ $cos(pi+x)=cospicosx-sinpisinx=(cosx*-1)-(sinx*0)=-cosx$ .

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How can I prove the identity for cos(x+pi)=-cos x ?

Using the angle sum and angle difference formulas

1 Answer

Explanation:

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