Question

Решите тригонометрию срочно. Даю 50 баллов!

Answer 1

Ответ:

$1)\ \ tg1,4\cdot ctg1,4+cos^2\Big(-\dfrac{2\pi}{3}\Big)-sin^2\dfrac{\pi}{3}-cos^2\dfrac{\pi}{3}=\\\\\\=1+cos^2\dfrac{2\pi}{3}-(sin^2\dfrac{\pi}{3}+sin^2\dfrac{\pi}{3})=1+cos^2(\pi -\dfrac{\pi}{3})-1=cos^2\dfrac{\pi}{3}=\Big(\dfrac{1}{2}\Big)^2=\dfrac{1}{4}$

$2)\ \ cost=0\\\\t=\dfrac{\pi}{2}+2\pi k\ ,\ k\in Z\ \ \ \ \ i\ \ \ \ t=-\dfrac{\pi}{2}+2\pi k\ ,\ k\in Z$

$3)\ \ 3\, ctg\dfrac{\pi}{4}-\dfrac{2}{3}\, tg^2\Big(-\dfrac{\pi }{3}\Big)=3\cdot 1-\dfrac{2}{3}\, tg^2\dfrac{\pi}{3}=3-\dfrac{2}{3}\cdot (\sqrt3)^2=3-2=1$