Question

Find all solutions in the interval [0, 2π).

sec2x - 2 = tan2x

a) No solution

b) x = pi/3

c) x = pi/4

d) x = pi/6

Answer 1

The answer is no solution.
Step-by-step explanation:
sec²x - 2 = tan²x
tan²x=sec²x-1
sec²x - 2 = sec²x-1
-2=-1

there is no solution

Answer 2

we have that
sec²x - 2 = tan²x--------> equation 1

and we know
identity-----------> tan²x=sec²x-1------------> equation 2

I substitute 2 in 1
sec²x - 2 = sec²x-1----------> -2=-1---------> no solution

the answer is the option a) No solution