Question

Вычислить............​

Answer 1

$1)\ \ sin\dfrac{7\pi}{12}-sin\dfrac{\pi}{12}=2\, sin\dfrac{\pi}{4}\cdot cos\dfrac{2\pi}{3}=2\cdot \dfrac{\sqrt2}{2}\cdot (-\dfrac{1}{2})=-\dfrac{\sqrt2}{2}\\\\\\2)\ \ tg\dfrac{5\pi}{12}+tg\dfrac{7\pi}{12}=\dfrac{sin75^\circ }{cos75^\circ}+\dfrac{sin105^\circ }{cos105^\circ }=\dfrac{sin75^\circ\cdot cos105^\circ +sin105^\circ \cdot cos75^\circ}{cos75^\circ \cdot cos105^\circ }=\\\\\\=\dfrac{sin180^\circ }{cos75^\circ \cdot cos105^\circ }=\dfrac{0}{cos75^\circ \cdot cos105^\circ }=0$

$3)\ \ \dfrac{sin2a+sin4a}{cos2a-sin4a}=\dfrac{2\, sin3a\cdot cosa}{cos2a-2sin2a\cdot cos2a}=\dfrac{2\, sin3a\cdot cosa}{cos2a\, (1-2sin2a)}\\\\\\\star \star \ \ \dfrac{sin2a+sin4a}{cos2a-cos4a}=\dfrac{2\, sin3a\cdot cosa}{2\, sin3a\cdot sina}=\dfrac{cosa}{sina}=tga$