Question

60 БАЛЛОВ!! Помогите пожалуйста преобразовать в произведение.

2 cos² a + √3 sin 2 a - 1

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Answer 1

Ответ:

$2cos^2\alpha+\sqrt3 sin2\alpha-1=2sin \left(\frac{\pi}{6}+2\alpha \right)$

Объяснение:

$2cos^2\alpha+\sqrt3 sin2\alpha-1=$

$2cos^2\alpha+\sqrt3 sin2\alpha-(sin^2\alpha+cos^2\alpha)=$

$2cos^2\alpha+\sqrt3 sin2\alpha-sin^2\alpha-cos^2\alpha=$

$cos^2\alpha+\sqrt3 sin2\alpha-sin^2\alpha=$

$cos2\alpha+2\cdot\frac{\sqrt3}{2}sin 2\alpha$

$cos2\alpha+2sin\frac{\pi}{3}sin 2\alpha=$

$2\cdot \frac{1}{2}cos2\alpha+2cos\frac{\pi}{6}sin 2\alpha=$

$2\cdot sin\frac{\pi}{6}cos2\alpha+2cos\frac{\pi}{6}sin 2\alpha=$

$2\cdot  \left(sin\frac{\pi}{6}cos2\alpha+cos\frac{\pi}{6}sin 2\alpha\right) =$

$2sin \left(\frac{\pi}{6}+2\alpha \right)$