Question

Вычислите 5sin120-tg60/2cos45*sin135
a) 1.5 корень3
б) 1.5 корень3
в) 1.5
г) - 1.5
д) корень3

Answer 1

$\frac{5Sin120^{o}-tg60^{o}}{2Cos45^{o}*Sin135^{o}}=\frac{5Sin(90^{o}+30^{0})-tg60^{o}}{2Cos45^{o}*Sin(90^{o}+45^{o})}=\frac{5Cos30^{o}-tg60^{0}}{2Cos45^{o}*Cos45^{o}}=\frac{5*\frac{\sqrt{3} }{2}-\sqrt{3}}{2*\frac{\sqrt{2}}{2}*\frac{\sqrt{2} }{2}}=\frac{2,5\sqrt{3}-\sqrt{3}}{1}=1,5\sqrt{3}$