Question 529078
solve the equation on the interval [0,2π] 
(tanx-1)(cosx+1)=0
FOIL
tanxcosx-cosx+tanx-1=0
tanx(cosx+1)-(cosx+1)=0
(cosx+1)(tanx-1)=0
..
cosx+1=0
cosx=-1
x=π
or
tanx-1
x=3&#960;/4 and 7&#960;/4 (reference angle &#960;/4 in quadrants II and IV where tan<1)