Question

- tan2x + sec2x = 1

Answer 1

- sin 2 x / cos 2 x + 1 / cos 2 x = 1
(1- sin 2 x ) / cos 2 x  = 1
1 - sin 2 x = cos 2 x
sin² x + cos² x - 2 sin x cos x = cos² x - sin² x
2 sin² x - 2 sin x cos x = 0   /:2
sin² x - sin x cos x = 0
sin x ( sin x - cos x ) = 0
sin x = 0,                 sin x - cos x = 0
x 1= k π,                sin x = cos x
k ∈ Z                       x 2 = π/4 + kπ,  k ∈ Z