Find all solutions in the interval [0, 2π). sec²x - 2 = tan²x

Solution:

Given,

Interval --- [0, 2π).

Equation --- sec²x - 2 = tan²x

We have

sec²x - 2 = tan²x --- (1)

We know the trigonometric identity

tan²x = sec²x - 1 --- (2)

Substituting (1) in (2), we get,

sec²x - 1 = sec²x - 2

-1 = -2

Therefore, there is no solution for this interval.

Find all solutions in the interval [0, 2π). sec²x - 2 = tan²x

Summary:

There is no solution for sec²x - 2 = tan²x in the interval [0, 2π).