I don't understand how do I solve for all real values of x with the following equation 2 tan² x - 3 sec x = 0 ? Thanks.

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Answer 1 · 2018-02-23T09:06:07

#x=2npi+-pi/3#

As #sec^x=1+tan^2x#, we have #tan^2x=sec^2x-1# and

#2tan^2x-3secx=0# becomes

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

or #(2secx+1)(secx-2)=0#

but #2secx+1!=0#

hence #secx=2=sec(pi/3)#

and #x=2npi+-pi/3#