(cos59o)) б) (1-ctg1o) (1-ctg2o)… (1-ctg44o)...

July 2022 1 11 Report

Вычислить:
а)(1-(соs61o)/(cos1o)) (1-(соs62o)/(cos2o))… (1-(соs119o)/(cos59o))
б) (1-ctg1o) (1-ctg2o)… (1-ctg44o)

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$(1-\frac{cos61}{cos1}) ( 1 - \frac{cos62}{cos2} ) (1-\frac{cos63}{cos3})*...*(1-\frac{cos119}{cos59}) \\ 
\frac{(cos1-cos61)(cos2-cos62)(cos3-cos63)*...*(cos59-cos119)}{cos1*cos2 * cos3*...*cos59}\\
\frac{ 2^{58}*(sin30)^{58}*sin31*sin32*sin33 *...*sin89}{cos59*cos58*cos57*...*cos1} = 1\\ 
$

$(1-ctg1)(1-ctg2)(1-ctg3) * ... * (1-ctg44) = \\\\
\frac{(cos1-sin1)(cos2-sin2)(cos3-sin3)*...*(cos44-sin44))}{ cos1*cos2*cos3*cos4*cos5*...*cos44 } = \\\\ 
\frac{2^{44}sin45^{44}*sin44 * sin43 *...*sin1}{cos44*cos43*cos43*...*cos1}=\\\\
 2^{22}*tg1*tg2*tg3*tg4*...*tg44$

Дальше можно преобразовать через котангенсы , но все равно кондова

2 votes Thanks 2

TTFT007 ты это в ворде печатал?

Матов Латекс функция

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