tex]...

June 2022 1 7 Report

Упростите выражение.
а) [tex] \frac{4sin3 \alpha sin2 \alpha }{sin4 \alpha -sin6 \alpha +sin2 \alpha } [/tex]

б)[tex](ctg \alpha +ctg \beta ) * (cos( \alpha - \beta )-(cos( \alpha + \beta ))[/tex]

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Freakazoid

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$\frac{4sin3asin2a}{sin4a-sin6a+sin2a}\\sin4a+sin2a=2sin3acosa;\\sin6a=sin(2*3a)=2sin3acos3a\\\frac{4sin3asin2a}{2sin3acosa-2sin3acos3a}=\frac{4sin3asin2a}{2sin3a(cosa-cos3a)}=\frac{2sin2a}{cosa-cos3a}\\cosa-cos3a=2sin2asina;\\\frac{2sin2a}{2sin2asina}=\frac{1}{sina}.$

$(ctga+ctgb)*(cos(a-b)-cos(a+b))\\\frac{sin(a+b)}{sinasinb}*(2*\frac{(cos(a-b)-cos(a+b)}{2})\\\frac{sin(a+b)}{sinasinb}*2sinasinb=2sin(a+b)$

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Andrey51 July 2022 | 0 Ответы

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