Question

x apartine (0,pi/2) cosx=tg(pi/3)*sinx aratati ca sinx=1/2​

Answer 1

Răspuns:

Explicație pas cu pas:

cosx/sinx=tg(pi/3)

ctgx= tg(pi/3)=ctg(pi/6)

x apartine (0,pi/2

x=pi/6, Q.E.D.

sin(pi/6)=1/2

Answer 2

$\it x\in(0,\ \dfrac{\pi}{2})\ \ \ \ \ \ \ (1)\\ \\ \\ cosx=tg(\dfrac{\pi}{3})sinx \Rightarrow \dfrac{cosx}{sinx}=\sqrt3 \Rightarrow ctgx=\sqrt3\ \ \ \ \ \ (2)\\ \\ \\ (1),\ (2) \Rightarrow x=\dfrac{\pi}{6};\ \ \ \ \ sin\dfrac{\pi}{6}=\dfrac{1}{2}$