Solve the equation. (Enter your answers as a comma-separated list. Use n as an integer constant. Enter your response in radians.)

Question

sec²(x) − 4 tan(x) = −2

Answer 1

1. Replace sec²(x) with 1+tan²(x) as sec²(x) = 1+tan²(x)
2. Doing so gives 1 + tan²(x) - 4tan(x) = -2
3. Add 2 to both sides and simplify: tan²(x) - 4tan(x) + 3 =0
4. Complete the square by splitting the middle term into factors that add up to the 3rd term: tan²(x) - 3tan(x) - 1tan(x) + 3 =0
5. Factor and simplify: (tan(x) -1)(tan(x)-3)=0
6. Solve for each:
7. tan(x)=1 : x = (π/4) and (5π/4)
8. tan(x)=3 : x =arctan(3) + πn where n is an integer

Answer 2

sec² x = 1 + tan² x, a Pythagorean Identity that should be on your cheat sheet.