Question

Нужен номер 5 и 6 . Подробное решение

Answer 1

$tg alpha -ctg alpha =-3. tg ^{2} alpha +ctg ^{2} alpha =? (tg alpha -ctg alpha ) ^{2} =(-3)^{2} tg ^{2} alpha -2tg alpha *ctg alpha +ctg ^{2} alpha =9$

$tg ^{2} alpha -2+ctg ^{2} alpha =9 tg ^{2} alpha +ctg ^{2} alpha =11$

5. b).  tgα=3.
$frac{sin alpha }{cos alpha } =3, sin alpha =3*cos alpha$

$frac{6sin alpha +5cos alpha }{4sin alpha -3cos alpha } = frac{6*(3cos alpha )+5cos alpha }{4*(3cos alpha )-3cos alpha } = frac{23cos alpha }{9cos alpha } = frac{23}{9}$

6. 
$arcsin0-arccos frac{ sqrt{2} }{2}- frac{arctg frac{ sqrt{3} }{3} }{arcctg sqrt{3} } =0- frac{ pi }{4} - frac{ frac{ pi }{6} }{ frac{ pi }{6} } =- frac{ pi }{4} -1$