Вычислить: 1)1+tg^2 (-П/6)/1+ctg^2 (-П/6) 2)3-sin^2 (- П/3)-cos^2 (-П/3)/2cos (-П/4)...

Решите задачу:

$1)\; \; \frac{1+tg^2(-\frac{\pi}{6})}{1+ctg^2(-\frac{\pi}{6})} = \frac{1+tg^2\frac{\pi}{6}}{1+ctg^2\frac{\pi}{6}} = \frac{1+\frac{1}{3}}{1+3} =\frac{4}{3\cdot 4}=\frac{1}{3}\\\\2)\; \; \frac{3-sin^2(-\frac{\pi}{3})-cos^2(-\frac{\pi}{3})}{2cos(-\frac{\pi}{4})} =\frac{3-(\; sin^2(-\frac{\pi}{3})+cos^2(-\frac{\pi}{3})\; )}{2cos\frac{\pi}{4}} = \frac{3-1}{2\cdot \frac{1}{2}} =2$

$3)\; \; cosa-ctga\cdot sin(-a)=cosa-\frac{cosa}{sina}\cdot (-sina)=\\\\=cosa+cosa=2cosa\\\\4)\; \; \underbrace {tg(-a)\cdot ctg(-a)}_{1}+cos^2(-a)+sin^2a=\\\\=1+\underbrace {cos^2a+sin^2a}_{1}=1+1=2$