Answer:
x = kπ
Step-by-step explanation:
tan²x sec²x + 2 sec²x − tan²x = 2
Use Pythagorean identity.
tan²x (1 + tan²x) + 2 (1 + tan²x) − tan²x = 2
Simplify.
tan²x + tan⁴x + 2 + 2 tan²x − tan²x = 2
tan⁴x + 2 tan²x = 0
tan²x (tan²x + 2) = 0
tan²x can't be negative, so the second factor cannot be 0.
tan²x = 0
tan x = 0
x = kπ
