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

Question

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

Answer 1

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