Question

cos x=1/7
cos y=13/14

x și y apartin (0;pi/2)

CALCULATI:
x-y=?​

Answer 1

$\it x,\ y\in\Big(0,\ \dfrac{\pi}{2}\Big)\\ \\ sinx=\sqrt{1-cos^2x}=\sqrt{1-\dfrac{1}{49}}=\sqrt{\dfrac{48}{49}}=\dfrac{4\sqrt3}{7}\\ \\ \\ siny=\sqrt{1-cos^2y}=\sqrt{1-\dfrac{169}{196}}=\sqrt{\dfrac{27}{196}}=\dfrac{3\sqrt3}{14}$

$\it cos(x-y)=cosxcosy+sinxsiny=\dfrac{1}{7}\cdot\dfrac{13}{14}+\dfrac{4\sqrt3}{7}\cdot\dfrac{3\sqrt3}{14}=\dfrac{13+36}{7\cdot7\cdot2}=\\ \\ \\ =\dfrac{49}{49\cdot2}=\dfrac{1}{2} \Rightarrow x-y=\dfrac{\pi}{3}$