Question

Aratati ca sin2x=4√2/9, stiind ca sinx=1/3 si x∈(0, π/2).

Answer 1

Doar ce e cu albastru scris :)

Answer 2

sin2x=2sinxcosx

sin²x+ cos²x=1

 sinx=1/3⇒ cos²x=1-sin²x⇒cos²x=1-(1/3)²⇒cos²x=1-$\frac{1}{9}$⇒cos²x=$\frac{25}{9}$⇒ cosx=+-  5/3


sin2x=2sinxcosx=2·$\frac{1}{3}$·$\frac{5}{3}$