Question

Упростить: 2sin2xsinx+cos3x
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Answer 1

Ответ:

$\cos(x + y) = \cos(x \ ) \times \cos(y) - \sin(x) \times \sin(y) \\ \cos(3x) = \cos(x + 2x) = \cos(x) \times \cos(2x) - \sin(x ) \times \sin(2x) \\ \cos(3x) + 2 \sin( x ) \times \sin(2x) = \cos(x) \times \cos(2x) - \sin(x ) \times \sin(2x) + 2 \sin(x) \times \sin(2x) = \cos(x) \times \cos(2x) + \sin(x) \times \sin(2x) = \cos(2x - x) = \cos(x)$