Question

алгебра помогите решить скрин прилагается

Answer 1

$6)\; \; tg(-\frac{\pi}{4})+cos(-\frac{\pi}{4})+sin(-\frac{\pi}{4})=-tg\frac{\pi}{4}+cos\frac{\pi}{4}-sin\frac{\pi}{4}=\\\\=-1+\frac{\sqrt2}{2}-\frac{\sqrt2}{2}=-1\\\\\\7)\; \; sin(-\frac{\pi}{6})- cos(-\frac{\pi}{3})-tg(-\frac{\pi}{6})=-sin\frac{\pi}{6}-cos\frac{\pi}{3}+tg\frac{\pi}{6}=\\\\=-\frac{1}{2}-\frac{1}{2}+\frac{\sqrt3}{3}=\frac{\sqrt3}{3}-1$

$8)\; \; sin(-\frac{3\pi}{2})+cos(-11\pi )=-sin\frac{3\pi}{2}+cos11\pi =-(-1)+cos(\underbrace {5\cdot 2\pi }_{period}+\pi )=\\\\=1+cos\pi =1-1=0\\\\\\9)\; \; tg(-780^\circ )-ctg(-390^\circ )=-tg(\underbrace {4\cdot 180^\circ }_{period}+60^\circ )+ctg(\underbrace {2\cdot 180^\circ }_{period}+30^\circ )=\\\\=-tg60^\circ +ctg30^\circ =-\sqrt3+\sqrt3=0$