sinx+siny+sinz+sin x=-4 then find the value of sin^400 x+sin^300 y+sin^200 z+sin^100 x. Can anyone give me hints on this sum.

Dear student

There is only one way ( sin x + sin y + sin z + sin x ) can be -4

Individually all values need to be -1

So,

Value of required expression is 1+1+1+1 = 4

Regards