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Why cos(-x)=cosx?Explain,please.

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sokolof | Student, Grade 11 | (Level 2) eNoter

Posted August 18, 2011 at 12:43 AM via web

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Why cos(-x)=cosx?Explain,please.

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted August 18, 2011 at 12:45 AM (Answer #1)

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We can write cos (-x) = cos (0-x), such as the following identity may now be used:

cos (a-b) = cos a*cos b + sin a*sin b

Let a = 0 and b = x

cos (0-x) = cos 0*cos x + sin 0*sin x

But cos 0 = 1 and sin 0 = 0.

cos (0 - x) = 1*cos x + 0*sin x

cos (0 - x) = cos x

Therefore, the identity cos(-x) = cos x is verified.

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