CosП/7-cos2 П/7+cos3 П/7

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Алгебра

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24 января, 10:06

CosП/7-cos2 П/7+cos3 П/7

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Ждан · Answer 1

Cosπ/7-cos2π/7+cos3π/7⇒π/7=α⇒

cosα-cos2α+cos3α = (cos3α+cosα) - cos2a=

=2cos (3α+α) / 2·cos (3α-α) / 2-cos2α=2cos2α·cosα-cos2α=

=cos2α (cosα-1) = (2cos²α-1) (cosα-1) = (2cos²π/7 - 1) (cosπ/7-1) ;