Вычислить
2sin3xcos5x-sin8x, если sinx-cosx = 0.3
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2sin3xcos5x-sin8x = 2*( sin(3x+5x) +sin(3x-5x) ) /2 -sin8x =
sin8x - sin2x -sin8x = - sin2x = (sinx -cosx)² -1 =0.3² -1 = 0.09 -1= - 0.91.
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можно и так (sinx - cosx)² = 0.3²⇔ sin²x -2sinx *cosx+cos²x = 0.09⇔
1 - sin2x = 0.09 ⇒ - sin2x = 0.09 - 1 = - 0.91