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only Integer solution is x=0
you know that sin(0)=0
sin(0)*sin(0)=sin^2(0)=0
same will be for any power
sin^100(0)=0
cos(0)=1 same reasoning as above
cos^100(0)=1
so,
sin^100(0)+cos^100(0)=1
0+1=1
1=1 ->true