Question

Решить: 4cos^2(31pi/6)+tg^2(11pi/3)+ctg^2(29pi/4)

Answer 1

$4cos^2\, \frac{31\pi}{6}+tg^2\, \frac{11\pi}{3}+ctg^2\, \frac{29\pi}{4}=\\\\=4cos^2(4\pi +\pi +\frac{\pi}{6})+tg^2(4\pi -\frac{\pi}{3})+ctg^2(7\pi +\frac{\pi}{4})=\\\\=4cos^2(\pi +\frac{\pi}{6})+tg^2(-\frac{\pi}{3})+ctg^2\frac{\pi}{4}=4(-cos\frac{\pi}{6})^2+(-tg\frac{\pi}{3})^2+1^2=\\\\=4cos^2\frac{\pi}{6}+tg^2\frac{\pi}{3}+1=4\cdot (\frac{\sqrt3}{2})^2+(\sqrt3)^2+1=\\\\=4\cdot \frac{3}{4}+3+1=7$