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Find all solutions of the equation in the interval [0, 2pi).
Sec^2x - secx = 2
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= .
Introduce new variable u = seq(x). Then your equation becomes
= ,
= .
Factor the left side. You will get
(u-2)*(u+1) = 0.
The solutions are
u = 2 and/or u = -1.
From this point you have two equations:
1) sec(x) = 2 ---> = 2 ---> cos(x) = ---> x = +/- + , k = 0, +/-1, +/-2, . . . and
2) sec(x) = -1 ---> = -1 ---> cos(x) = ---> x = + , k = 0, +/-1, +/-2, . . .
Answer. x = +/- + , k = 0, +/-1, +/-2, . . . and
x = , k = 0, +/-1, +/-2, . . .
Solved.