Question

Знайдіть значення виразу

Answer 1

$\sqrt{\Big(1-2Cos\dfrac{\pi }{6} \Big)^{2} }-\sqrt{\Big(1+2Sin\dfrac{\pi }{3}\Big)^{2}}=\Big|1-2Cos\dfrac{\pi }{6}\Big|-\Big|1+2Sin\dfrac{\pi }{3}\Big|=\\\\=\Big|1-2\cdot\dfrac{\sqrt{3} }{2}\Big|-\Big|1+2\cdot\dfrac{\sqrt{3} }{2}\Big|=\Big|1-\sqrt{3}\Big|-\Big|1+\sqrt{3}\Big|=\\\\=\sqrt{3}-1-1-\sqrt{3}=\boxed{-2}$