Question

Решите задания, пожалуйста. 60 баллов

Answer 1

$3)\; \; cos(\frac{\pi }{6}+a)-\frac{\srqt3}{2}\cdot cosa=cos\frac{\pi }{6}\cdot cosa-sin\frac{\pi }{6}\cdot sina-\frac{\sqrt3}{2}\cdot cosa=\\\\=\frac{\sqrt3}{2}\cdot cosa-\frac{1}{2}\cdot sina-\frac{\sqrt3}{2}\cdot cosa=-\frac{sina}{2}$

$4)\; \; \sqrt2sin(\frac{\pi }{4}+a)=\sqrt2\cdot (sin\frac{\pi }{4}\cdot cosa+cos\frac{\pi }{4}\cdot sina)=\\\\=\sqrt2\cdot (\frac{\sqrt2}{2}\cdot cosa+\frac{\sqrt2}{2}\cdot sina)=cosa+sina\\\\5)\; \; sin120^\circ \cdot cos30^\circ +sin30^\circ \cdot cos120^\circ =sin(120^\circ +30^\circ )=sin150^\circ =\\\\=sin(90^\circ +60^\circ )=-cos60^\circ =-\frac{\sqrt3}{2}\\\\-\frac{\sqrt3}{2}=-\frac{\sqrt3}{2}$