Solve# sec^2 x-3secx + 2=0# for all solutions [0, 2pi)?

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Answer 1 · 2016-10-14T15:15:29

#sec^2 x-3secx + 2=0 #

#=>sec^2 x-2secx-secx + 2=0 #

#=>sec x(secx-2)-1(secx - 2)=0 #

#=>(secx-2)(secx - 1)=0 #

when
#secx-2=0#

#=>secx=2#

#=>cosx=1/2=cos(pi/3)=cos(2pi-pi/3)#

So #x = pi/3 and x= (5pi)/3#

Again when

#" "(secx - 1)=0#

#=>cosx=1=cos(o)" as "0<= x < 2pi#

So #x=0 #