Question

Вычислите: ( cos 30+ sin30)^2


​

Answer 1

$\displaystyle\bf\\\Big(Sin30^\circ+Cos30^\circ\Big)^{2} =Sin^{2} 30^\circ+2Sin30^\circ Cos30^\circ+Cos^{2} 30^\circ=\\\\\\=\underbrace {\Big(Sin^{2} 30^\circ+Cos^{2} 30^\circ\Big)}_{1}+\underbrace{2Sin30^\circ Cos30^\circ}_{Sin60^\circ}=1+Sin60^\circ=\\\\\\=1+\frac{\sqrt{3} }{2} =\frac{2+\sqrt{3} }{2}$