Prove that sinx + siny +sinz - sin(x+y+z) = 4sin((x+y/2)sin((y+z/2)sin((z+x/2)

We have to prove that,

sinx+siny+sinz-sin(x+y+z)=4sin((x+y)/2)sin((y+z)/2)sin((z+x)/2)

Keep in mind

LHS:

As, in a triangle , sum of all interior angles is 180°.

x+y+z=180°

x+y=180°-z

Similarly,

and, cos(x-y)+cos(x+y)=2 cos x cos y

=Sinx +Sin y +Sin z-sin (180°)

=Sin x +SIn y +Sin z-0

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        i think it is referred as the 8th wonder of the world because each of the terra cotta warriors was not the same. they each had many things with their physical stature, like different height, armor, and different characteristics, which were all different. what makes it interesting is that there were 8,000 soldiers in that tomb. so making that many soldiers for the emperor meant a-lot to the emperor. it means that their is strength in numbers now matter how different.

hope it : p