trip
posted by bob .
for sin2x+cosx=0, use doubleangle or halfangle formula to simplify the equation and then find all solutions of the equation in the interval (0,2Pie)

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sin2x= 2sinxcosx
cosx(2sinx+1)=0
cosx=0 so x=0, PI, 2PI
sinx=1/2, so x=3PI/2 check that.