Question

Rozwiąż równanie

a) sin2xtgx=sinx

Answer 1

Sin2x tgx = sinx
sin2x = 2sinxcosx
tgx = sinx/cosx
2sinxcosx × sinx/cosx = sinx
2sin²x = sinx
2sin²x - sinx = 0
sinx(2sinx - 1) = 0
sinx = 0  ∨ 2sinx -1 = 0  ⇒ 2sinx = 1  ⇒ sinx = 1/2
x₁ = kπ (k×180°)
x₂ = π/6 + 2kπ  (30° + k×360°)
x₃ = 5/6 π + 2kπ  (150° + k×360°)