Question

se considera numerele reale a si b astfel incat a+b=π/3. Aratati ca 2cosb=cosa+√3sina

Answer 1

$\it b= \dfrac{\pi}{3}-a$

$\it cos b= cos(\dfrac{\pi}{3}-a) =cos \dfrac{\pi}{3}cos a + \sin\dfrac{\pi}{3} \it\sin a \ \Longrightarrow$

$\it {\Longrightarrow cos b = \dfrac{1}{2}cos a +\dfrac{\sqrt3}{2} sin a \ |_{\cdot2}\Longrightarrow 2b = cos a + \sqrt3 sin a}\ .$