wzory redukcyjne

[mrowkazzzzz]

obliczyc

\(\displaystyle{ \frac{cos 315 \cdot -sin(3 \pi + \frac{ \pi }{4})sin570 \cdot }{(cos3 \pi )sin600 \cdot }}\)

[loitzl9006]

\(\displaystyle{ = - \frac{cos(360-45) \cdot sin(360+180-45) \cdot sin(360+180+30)}{cos(360+180) \cdot sin360+180+60)} = - \frac{cos(360-45) \cdot sin(180-45) \cdot sin(180+30)}{cos(180) \cdot sin(180+60)} = -\frac{cos45 \cdot sin45 \cdot (-sin30)}{cos(180) \cdot (-sin60)} = - \frac{ \frac{ \sqrt{2} }{2} \cdot \frac{ \sqrt{2} }{2} \cdot (- \frac{1}{2} )}{-1 \cdot (- \frac{ \sqrt{3} }{2} )} = - \frac{ \frac{-1}{4} }{ \frac{ \sqrt{3} }{2} } = \frac{ \frac{1}{4} }{ \frac{ \sqrt{3} }{2} }= \frac{1}{4} \cdot \frac{2}{ \sqrt{3} } = \frac{1}{2 \sqrt{3} } = \frac{ \sqrt{3} }{6}}\)