Find all solutions of the equation in the interval 0 2pi En

Find all solutions of the equation in the interval [0, 2pi). (En NO SOLUTION.) 8 sec^2 x 8 sec x = 16 Find all solutions of the equation in the interval [0, 2pi). (Ente NO SOLUTION.)

Solution

8sec²x -8secx =16

8(sec²x -secx) =16

(sec²x -secx) =16/8

(sec²x -secx) =2

sec²x -secx -2=0

sec²x -2secx+secx -2=0

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

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

secx=2=>x =2npi+(pi/3),2npi-(pi/3)

secx =-1 =>x=2npi-pi,2npi +pi