First, we can simplify the expression by using the trigonometric identity
[ \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)} ]
Therefore, we have:
[ tg(225) \times \sin(780) \times \cos(810) = \frac{\sin(225)}{\cos(225)} \times \sin(780) \times \cos(810) ]
Since (\sin(225) = -\frac{\sqrt{2}}{2}) and (\cos(225) = -\frac{\sqrt{2}}{2}), we can substitute these values into the expression:
[ \frac{-\frac{\sqrt{2}}{2}}{-\frac{\sqrt{2}}{2}} \times \sin(780) \times \cos(810) ]
Now, simplify the expression:
[ 1 \times \sin(780) \times \cos(810) = \sin(780) \times \cos(810) ]
Finally, (\sin(780)) is equal to (\sin(360+420) = \sin(420) = \sin(60) = \frac{\sqrt{3}}{2}), and (\cos(810)) is equal to (\cos(720+90) = \cos(90) = 0).
[ \sin(780) \times \cos(810) = \frac{\sqrt{3}}{2} \times 0 = 0 ]
Therefore, the final answer is 0.
First, we can simplify the expression by using the trigonometric identity
[ \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)} ]
Therefore, we have:
[ tg(225) \times \sin(780) \times \cos(810) = \frac{\sin(225)}{\cos(225)} \times \sin(780) \times \cos(810) ]
Since (\sin(225) = -\frac{\sqrt{2}}{2}) and (\cos(225) = -\frac{\sqrt{2}}{2}), we can substitute these values into the expression:
[ \frac{-\frac{\sqrt{2}}{2}}{-\frac{\sqrt{2}}{2}} \times \sin(780) \times \cos(810) ]
Now, simplify the expression:
[ 1 \times \sin(780) \times \cos(810) = \sin(780) \times \cos(810) ]
Finally, (\sin(780)) is equal to (\sin(360+420) = \sin(420) = \sin(60) = \frac{\sqrt{3}}{2}), and (\cos(810)) is equal to (\cos(720+90) = \cos(90) = 0).
[ \sin(780) \times \cos(810) = \frac{\sqrt{3}}{2} \times 0 = 0 ]
Therefore, the final answer is 0.