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

There is no solution because of the identity

(sec^2)x - (tan^2)x = 1.

You would otherwise end up with 1 = 2

Answer 2

Rearranging your equation, you would have:

(sec^2)x - (tan^2)x = 2

And the left side is equal to 1 always.

Answer 3

ok thank you!!

Answer 4

You're welcome!