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Answer 1 · 2018-02-12T21:07:24

#x=0, 3/4pi, pi, 7/4pi#

We want to find the solutions of the equation

#sec^2(x)+tan(x)=1#

Use the trigonmetric identity #color(blue)(sec^2(x)=tan^2(x)+1)#

#tan^2(x)+1+tan(x)=1#

#<=>tan^2(x)+tan(x)=0#

#<=>tan(x)(tan(x)+1)=0#

Therefore

#tan(x)=0 or tan(x)=-1#

By the inverse tangent with #x in [0,2pi)#

#x=0, 3/4pi, pi, 7/4pi#