Question

Fie x apartine R, astfel incat sinx= 1/2 + cos x. Calculati sin 2x

Answer 1

sinx = 1/2 + cosx
cosx^2 = 1 - sinx^2
sinx^2 = 1/4 + cosx + cosx^2
sinx^2 = 1 - cosx^2
1-cosx^2 = 1/4 + cosx + cosx^2
2cosx^2 + cosx - 3/4 = 0
Δ = 1 + 3/2
Δ = 5/2
x1 = (√10 - 2)/8
x2 = -(√10 + 2)/8

cosx = (√10 - 2)/8
sinx = 1/2 + (√10 - 2)/8
sinx = (√10+2)/8 ⇒ sin 2x = (√10 + 2) / 4