2sin^2 x-5sinx*cosx+3cos^2 x=o

Question

2sin^2 x-5sinx*cosx+3cos^2 x=o

Answer 1

2sin^2 x-5sinx*cosx+3cos^2 x=0 | : Cos²x
2tg²x - 5tgx +3 = 0
tgx = t
2t² - 5t +3 = 0
D = b² -4ac = 25 -24 = 1
t₁ = 6/4 = 1,5                                 t₂ = 1
a) tgx = 1,5                                  б) tgx = 1
x = arctg1,5 + πk , k ∈Z           x = π/4 + πn , n ∈Z

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