Задача 57454 ...

5f3ea7e3faf909182968ddd9

27.01.2021 20:42:50

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sin5cos7-sin10cos2=-sin5cos3

По формуле:

[r] sin α *cos β =(1/2) sin ( α + β )+ (1/2) sin ( α - β )[/r]


sin5cos7=(1/2) sin 12+(1/2)sin(-2)=(1/2)sin12-(1/2)sin2

sin10cos2=(1/2)sin12+(1/2)sin8

sin5cos3=(1/2)sin8+(1/2)sin2


(1/2)sin12-(1/2)sin2-(1/2)sin12-(1/2)sin8=-(1/2)sin8-(1/2)sin2 - верно.

Значит и данное равенство верно