Since sin(225)=−22\sin(225) = -\frac{\sqrt{2}}{2}sin(225)=−22 and cos(225)=−22\cos(225) = -\frac{\sqrt{2}}{2}cos(225)=−22, we can substitute these values into the expression:
Finally, sin(780)\sin(780)sin(780) is equal to sin(360+420)=sin(420)=sin(60)=32\sin(360+420) = \sin(420) = \sin(60) = \frac{\sqrt{3}}{2}sin(360+420)=sin(420)=sin(60)=23, and cos(810)\cos(810)cos(810) is equal to cos(720+90)=cos(90)=0\cos(720+90) = \cos(90) = 0cos(720+90)=cos(90)=0.
First, we can simplify the expression by using the trigonometric identity
tan(θ)=sin(θ)cos(θ) \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)} tan(θ)=cos(θ)sin(θ)
Therefore, we have:
tg(225)×sin(780)×cos(810)=sin(225)cos(225)×sin(780)×cos(810) tg(225) \times \sin(780) \times \cos(810) = \frac{\sin(225)}{\cos(225)} \times \sin(780) \times \cos(810) tg(225)×sin(780)×cos(810)=cos(225)sin(225) ×sin(780)×cos(810)
Since sin(225)=−22\sin(225) = -\frac{\sqrt{2}}{2}sin(225)=−22 and cos(225)=−22\cos(225) = -\frac{\sqrt{2}}{2}cos(225)=−22 , we can substitute these values into the expression:
−22−22×sin(780)×cos(810) \frac{-\frac{\sqrt{2}}{2}}{-\frac{\sqrt{2}}{2}} \times \sin(780) \times \cos(810) −22 −22 ×sin(780)×cos(810)
Now, simplify the expression:
1×sin(780)×cos(810)=sin(780)×cos(810) 1 \times \sin(780) \times \cos(810) = \sin(780) \times \cos(810) 1×sin(780)×cos(810)=sin(780)×cos(810)
Finally, sin(780)\sin(780)sin(780) is equal to sin(360+420)=sin(420)=sin(60)=32\sin(360+420) = \sin(420) = \sin(60) = \frac{\sqrt{3}}{2}sin(360+420)=sin(420)=sin(60)=23 , and cos(810)\cos(810)cos(810) is equal to cos(720+90)=cos(90)=0\cos(720+90) = \cos(90) = 0cos(720+90)=cos(90)=0.
sin(780)×cos(810)=32×0=0 \sin(780) \times \cos(810) = \frac{\sqrt{3}}{2} \times 0 = 0 sin(780)×cos(810)=23 ×0=0
Therefore, the final answer is 0.