Найти тангенс, если 25 синyс^2+10 косинус^2=13

25sin²x + 10cos²x = 13

15sin²x + 10sin²x + 10cos²x = 13

15sin²x + 10 (sin²x + cos²x) = 13

sin²x + cos²x = 1

15sin²x + 10 = 13

15sin²x = 13 - 10 = 3

5sin²x = 1

sin²x = 1/5

cos²x = 1 - sin²x = 1 - 1/5 = 4/5

tg²x = sin²x/cos²x = (1/5) / (4/5) = 1/4

tgx₁ = 1/2

tgx₂ = - 1/2