Question

упростите

((sinA/1+cosA) +(sinA/1-cosA))×sin2a

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Answer 1

$\left(\dfrac{\sin \alpha}{1+\cos \alpha}+\dfrac{\sin \alpha}{1-\cos \alpha}\right)\sin 2\alpha=\dfrac{\sin \alpha-\cos \alpha \sin\alpha +\sin \alpha+\sin \alpha\cos\alpha}{1-\cos^2\alpha}\cdot \\ \\ \\ \cdot \sin 2\alpha=\dfrac{2\sin \alpha}{\sin^2\alpha}\cdot 2\sin\alpha\cos\alpha=4\cos \alpha$