Question

ДАЮ 50 БАЛЛОВ! Упростить

Answer 1

$\displaystyle\bf\\\frac{2-Sin^{2} \Big(-\dfrac{\pi }{6} \Big)+Cos^{2} \Big(-\dfrac{\pi }{3} \Big)}{2Cos\Big(-\dfrac{\pi }{3} \Big)+Sin\Big(-\dfrac{\pi }{6} \Big)}= \frac{2-Sin^{2} \dfrac{\pi }{6} +Cos^{2} \dfrac{\pi }{3}}{2Cos\dfrac{\pi }{3} -Sin\dfrac{\pi }{6}}= \\\\\\=\frac{2-\Big(\dfrac{1}{2}\Big)^{2} +\Big(\dfrac{1}{2} \Big)^{2} }{2\cdot \dfrac{1}{2} -\dfrac{1}{2} } =\frac{2-\dfrac{1}{4} +\dfrac{1}{4} }{1-\dfrac{1}{2} } =2:\frac{1}{2}=2\cdot 2=4\\\\\\Otvet \ : \ 4$