Question

Вычислите: sin110 cos70- sin5 cos35

Answer 1

$Sin110^{o}Cos70^{o}-Sin5^{o}Cos35^{o}=\frac{1}{2}(Sin(110^{o}-70^{o})+Sin(110^{o}+70^{o}))-\frac{1}{2}(Sin(5^{o} -35^{o})+Sin(5^{o}+35^{o}))=\frac{1}{2}(Sin40^{o}+Sin180^{o}+Sin30^{o}-Sin40^{o})=\frac{1}{2}(Sin180^{o}+Sin30^{o})=\frac{1}{2}(0+\frac{1}{2})=\frac{1}{4}$