Вычислить. 30 баллов!. Created by 2400. algebra-ru

Вычислить. 30 баллов!...

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July 2022 1 3 Report

Вычислить. 30 баллов!

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oganesbagoyan

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Вычислить
cos(2arctg( -8/15) )
-------
B =cos(2arctg( -8/15) )= cos(-2arctg(8/15) )= cos(2arctg(8/15))=cos2α =
2cos²α -1 ,где α =arctg(8/15) * * * -π/2 < α <π/2 * * *
tgα =tg(arctg(8/15)) = 8/15 ⇒ cos²α =1/(1+tg²α) =1 /(1+(8/15)²) =
15² / (225+64)=15 ²/289 = (15/17)²
следовательно :
B =2cos²α -1 =2*(15/17)² -1 =2*225/289 -1 =450/289 -1 =161/289.

ответ : 161/289.

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