Question

Найдите tg²α,если 4sin²α+9cos²α=6

Answer 1

4Sin²x + 9Cos²x = 6
(4Sin²x + 4Cos²x) + 5Cos²x = 6
4(Sin²α + Cos²α) + 5Cos²α = 6
Sin²α + Cos²α = 1 , значит
4 + 5Cos²α = 6
5Cos²α = 2
Cos²α = 2/5
$1 + tg ^{2} alpha = frac{1}{Cos alpha ^{2} }$
$tg ^{2} alpha = frac{1}{Cos ^{2} alpha } -1= frac{1}{ frac{2}{5} }-1= frac{5}{2}-1= frac{3}{2}=1,5$

Answer 2

Спасибо...