sin(x)/(cos(x)+1) + cos(x)/(sin(x)+1) = 1

sin^2(x) + sin(x) + cos^2(x) + cos(x) = cos(x)sin(x) + cos(x) + sin(x) +1

(sin^2(x) + cos^2(x) =1) Therefore;

1 +sin(x) + cos(x) = cos(x)sin(x) + sin(x) +cos(x) +1

Cancelling out on both sides

cos(x)sin(x) = 0

Solution: cos(x)=0 x=pi/2 + kpi sin(x)=0 x= 0+ kpi