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0= sin (pi)x + cos (pi)x

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2 Answers

Another solution.
sinΠx+cosΠx=0
sinΠx+cosΠx=sinΠx+sin(Πx+Π/2)
=2sin(Πx+Π/4)cos(-Π/4)=0
or sin(Πx+Π/4)=0 or Πx+Π/4=k∏ or x+1/4=k an integer
x=k-1/4 which falls in the interval (-1,3) for k=0,1,2,3 giving
x=-1/4, 3/4, 1 3/4, 2 3/4