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упростите выражение

6sin(2x -π/6)cos(3x+π/3) -3sin(5x+π/6)

Ответ:  - 3cosx

Объяснение:  * * *  sinα cosβ = ( sin(α+β) +sin(α-β) ) /2 * * *

6sin(2x -π/6)cos(3x+π/3) -3sin(5x+π/6) =

=6 ( sin(2x -π/6+3x+π/3)+  sin(2x -π/6-3x- π/3) ) /2 -3sin(5x+π/6) =

= 3sin(5x+π/6) +3sin(-x -π/2) - 3sin(5x+π/6) = -3sin(π/2 +x) = - 3cosx .

Ответ: -3cosx

Объяснение: