Sec^2(x)-sec(x)=2?

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Answer 1 · 2018-04-27T00:18:20

Within the interval #0 < x < +-2pi#,

#x=+-pi/3, +-(5pi)/3, +-pi#

.

#sec^2x-secx=2#

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

Let #secx=z#

#z^2-z-2=0#

#(z-2)(z+1)=0#

#z=2 and -1#

#secx=2, :. 1/cosx=2, cosx=1/2, x=+-pi/3, +-(5pi)/3#

#secx=-1, :. 1/cosx=-1, cosx=-1, x=+-pi#