Question

Вычислить...........​

Answer 1

$1)\ \ cos105^\circ+cos75^\circ =cos(180^\circ-75^\circ)+cos75^\circ =-cos75^\circ +cos75^\circ =0\\\\\\2)\ \ sin105^\circ -sin75^\circ =sin(180^\circ-75^\circ)-sin75^\circ =sin75^\circ -sin75^\circ =0$

$3)\ \ cos\frac{11\pi}{12}-cos\dfrac{5\pi}{12}=cos\Big(\pi -\dfrac{\pi}{12}\Big)-cos\dfrac{5\pi}{12}=\Big[\; \dfrac{\pi}{12}=15^\circ \ ,\ \dfrac{5\pi}{12}=75^\circ \; \Big]=\\\\\\=-cos\dfrac{\pi}{12}-cos\dfrac{5\pi}{12}=-cos15^\circ -cos75^\circ =-2\cdot cos\dfrac{15^\circ +75^\circ}{2}\cdot cos\dfrac{75^\circ -15^\circ }{2}=\\\\\\=-2\cdot cos45^\circ \cdot cos30^\circ =-2\cdot \dfrac{\sqrt2}{2}\cdot \dfrac{\sqrt3}{2}=-\dfrac{\sqrt6}{2}$