Question

Главный мозг , помоги , алгебра, 10 класс​

Answer 1

Ответ:

$1)\ \sin225^\circ -6cos120^\circ =sin(180^\circ +45^\circ )-6cos(180^\circ -60^\circ )=\\\\=-sin45^\circ +6cos60^\circ =-\dfrac{\sqrt2}{2}+6\cdot \dfrac{\sqrt3}{2}=\dfrac{6\sqrt3-\sqrt2}{2}\\\\\\2)\ \ sin\Big(-\dfrac{11\pi }{3}\Big)\cdot cos\dfrac{13\pi }{4}=-sin\Big(4\pi -\dfrac{\pi}{3}\Big)\cdot cos\Big(4\pi +\dfrac{\pi}{3}\Big)=\\\\=sin\dfrac{\pi}{3}\cdot cos\dfrac{\pi}{3}=\dfrac{\sqrt3}{2}\cdot \dfrac{1}{2}=\dfrac{\sqrt3}{4}$

$3)\ \ sin463^\circ \cdot cos373^\circ +cos103^\circ \cdot sin193^\circ =\\\\=sin(360^\circ +90^\circ +13^\circ )\cdot cos(360^\circ -13^\circ )+cos(90^\circ +13^\circ )\cdot sin(180^\circ +13^\circ )=\\\\=-cos13^\circ \cdpt cos13^\circ +sin13^\circ \cdot sin13^\circ =-(cos^213^\circ -sin^213^\circ )=-cos26^\circ$

$4)\ \ \dfrac{sin148^\circ \cdot sin168^\circ +cos12^\circ \cdot cos212^\circ }{sin110^\circ \cdot cos336^\circ +cos250^\circ \cdt sin24^\circ }=\\\\\\=\dfrac{sin(180^\circ -32^\circ )\cdot sin(180^\circ -12^\circ )+cos12^\circ \cdot cos(180^\circ +32^\circ )}{sin(180^\circ -70^\circ )\cdot cos(360^\circ -24^\circ )+cos(180^\circ +70^\circ )\cdot sin 24^\circ }=$

$=\dfrac{sin32^\circ \cdot sin12^\circ -cos12^\circ \cdot cos32^\circ }{sin70^\circ \cdot cos24^\circ -cos70^\circ \cdot sin24^\circ }=\dfrac{-cos\, 44^\circ }{sin\, 46^\circ }$